<PAGE>   1
                                                                    EXHIBIT 10.5

                                                                  EXECUTION COPY

================================================================================


                          MBIA INSURANCE CORPORATION,
                                  as Insurer,


                         CAPITAL ONE AUTO FINANCE, INC.
                                      and


                       CAPITAL ONE AUTO RECEIVABLES, LLC
                               as Issuer Parties


                                      and


                        BANC OF AMERICA SECURITIES LLC,
                     as Representative of the Underwriters


                           INDEMNIFICATION AGREEMENT


                                  $850,000,000
                     Capital One Auto Finance Trust 2001-A
               Automobile Receivable-Backed Notes, Series 2001-A
               Class A-1 Notes, Class A-2 Notes, Class A-3 Notes
                              and Class A-4 Notes


                           Dated as of July 12, 2001


================================================================================

<PAGE>   2
                           INDEMNIFICATION AGREEMENT

         This AGREEMENT, dated as of July 12, 2001 is between MBIA INSURANCE
CORPORATION (the "Insurer"), as the Insurer under the Note Guaranty Insurance
Policy (the "Policy") issued in connection with the Offered Notes described
below, Capital One Auto Finance, Inc. ("COAF"), Capital One Auto Receivables,
LLC, ("COAR," and together with COAF, the "Issuer Parties") and BANC OF AMERICA
SECURITIES LLC ("Bane of America"), as Representative of the Underwriters (the
"Representative") on behalf of the Underwriters (as defined below).

         Section 1. DEFINITIONS. As used in this Agreement, the following terms
shall have the respective meanings stated herein, unless the context clearly
requires otherwise, in both singular and plural form, as appropriate Capitalized
terms used in this Agreement but not otherwise defined herein will have the
meanings ascribed to such terms in the Indenture (as described below).

         "Act" means the Securities Act of 1933, as amended, together with all
related rules and regulations.

         "Agreement" means this Indemnification Agreement by and between the
Insurer and the Representative of the Underwriters.

         "Indemnified Party" means any party entitled to any indemnification
pursuant to Section 5 below, as the context requires.

         "Indemnifying Party" means any party required to provide
indemnification pursuant to Section 5 below, as the context requires.

         "Indenture" means the Indenture dated as of July 26, 2001 by and
between the Wilmington Trust Company, as Owner Trustee, and Wells Fargo Bank
Minnesota, National Association, as Indenture Trustee.

         "Insurance Agreement" means the Insurance Agreement, dated as of July
26, 2001 by and among the Insurer, the Owner Trustee, the Seller, the
Transferor, the Servicer, the Indenture Trustee and Owner Trustee.

         "Insurer Party" means the Insurer and its respective parents,
subsidiaries and affiliates and any shareholder, director, officer, employee,
agent or any "controlling person" (as such term is used in the Act) of any of
the foregoing.

         "Issuer Party" means each of COAF and COAR and its parent,
subsidiaries, and affiliates and any member, shareholder, director, officer,
employee, agent or any "controlling person" (as such term is used in the Act) of
any of the following.
<PAGE>   3
         "Losses" means (i) any actual out-of-pocket loss paid by the party
entitled to indemnification or contribution hereunder and (ii) any actual
out-of-pocket costs and expenses paid by such party, including reasonable fees
and expenses of its counsel, to the extent not paid, satisfied or reimbursed
from funds provided by any other Person (provided that the foregoing shall not
create or imply any obligation to pursue recourse against any such other
Person).

         "Offered Notes" means the Capital One Auto Finance Trust 2001-A
Automobile Receivable-Backed Notes, Series 2001-A, Class A-l, Class-A-2,
Class-A-3 and Class-A-4, issued in accordance with the provisions of the
Indenture.

         "Person" means any individual, partnership, joint venture, corporation,
trust or unincorporated organization or any government or agency or political
subdivision thereof.

         "Prospectus Supplement" means the Preliminary Prospectus Supplement
dated July 10, 2001 and the Prospectus Supplement dated July 12, 2001 with
respect to the Offered Notes.

         "Servicer" means Capital One Auto Finance, Inc. as the Servicer of the
Receivables or any other Eligible Servicer acting as servicer pursuant to the
Servicing Agreement. Unless the context otherwise requires "Servicer" also
refers to any successor Servicer appointed under the Indenture or pursuant to
the Servicing Agreement.

         "Servicing Agreement" means the Servicing Agreement dated as of July
26, 2001 by and among the Owner Trustee, the Indenture Trustee and the Servicer.

         "Underwriter Party" means, with respect to the Underwriters, each such
Underwriter and its parent, subsidiaries and affiliates and any shareholder,
director, officer, employee, agent or "controlling person" (as such term is used
in the Act) of any of the foregoing.

         "Underwriting Agreement" means the Underwriting Agreement by and among
COAF, Capital One Auto Receivables, LLC and Bane of America LLC, as
representative for the Underwriters, dated as of July 12, 2001.

         "Underwriters" and "Underwriter" means, in plural form, Banc of America
Securities LLC ("Banc of America"), Credit Suisse First Boston Corporation
("CSFB"), Deutsche Bank Alex. Brown Inc. ("Deutsche Bank") and First Union
Securities, Inc. ("First Union") and in singular form, each of Banc of America,
CSFB, Deutsche Bank and First Union.

         Section 2. REPRESENTATIONS AND WARRANTIES OF THE INSURER. The Insurer
represents and warrants to each Underwriter and the each Issuer Party as
follows:

                  (a) Organization and Licensing. The Insurer is a duly
incorporated and existing New York stock insurance company licensed to do
business in the State of New York and is in good standing under the laws of such
state.


                                       2
<PAGE>   4

                  (b) Corporate Power. The Insurer has the corporate power and
authority to issue the Policy and execute and deliver this Agreement and to
perform all of its obligations hereunder and thereunder.

                  (c) Authorization; Approvals. The issuance of the Policy and
the execution, delivery and performance of this Agreement have been duly
authorized by all necessary corporate proceedings. No further approvals or
filings of any kind, including, without limitation, any further approvals of or
further filings with any governmental agency or other governmental authority, or
any approval of the Insurer's board of directors or stockholders, are necessary
for the Policy and this Agreement to constitute the legal, valid and binding
obligations of the Insurer.

                  (d) Enforceability. The Policy, when issued, and this
Agreement will each constitute a legal, valid and binding obligation of the
Insurer, enforceable in accordance with its terms, subject to applicable laws
affecting the enforceability of creditors' lights generally.

                  (e) Financial Information. The consolidated financial
statements of the Insurer and its subsidiaries as of December 31, 2000 and
December 31, 1999 and for each of the three years in the period ended December
31, 2000 incorporated by reference in the Prospectus Supplement (the "Insurer
Audited Financial Statements"), fairly present in all material respects the
financial condition of the Insurer as of such date and for the period covered by
such statements in accordance with generally accepted accounting principles
consistently applied. The consolidated financial statements of the Insurer and
its subsidiaries as of March 31, 2001 and for the three month periods ended
March 31, 2001 and March 31, 2000 incorporated by reference in the Prospectus
Supplement (the "Insurer Unaudited Financial Statements", the Insurer Audited
Financial Statements and the Insurer Unaudited Financial Statements are referred
to herein as the "Insurer Financial Statements") present fairly in all material
respects the financial condition of the Insurer as of such date and for the
period covered by such statements in accordance with generally accepted
accounting principles applied in a manner consistent with the accounting
principles used in preparing the Insurer Audited Financial Statements, and since
March 31, 2001, there has been no material change in such financial condition of
the Insurer which would materially and adversely affect its ability to perform
its obligations under the Policy.

                  (f) Insurer Information. The information in the Prospectus
Supplement of the date hereof under the caption "THE NOTE GUARANTY INSURANCE
POLICY AND THE NOTE INSURER" (the "Insurer Information") is limited and does not
purport to provide the scope of disclosure required to be included in a
prospectus for a registrant under the Securities Act of 1933, in connection with
the public offer and sale of securities of such registrant. Within such limited
scope of disclosure, the Insurer Information does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements therein, in light of the circumstances under which they were
made, not misleading.

                  (g) No Litigation. There are no actions, suits, proceedings or
investigations pending or, to the best of the Insurer's knowledge, threatened
against it at law or in equity or


                                       3
<PAGE>   5


before or by any court, governmental agency, board or commission or any
arbitrator which, if decided adversely, would materially and adversely affect
its condition (financial or otherwise) or operations of it or would materially
and adversely affect its ability to perform its obligations under this Agreement
or the Policy.

         Section 3. REPRESENTATIONS AND WARRANTIES OF THE UNDERWRITERS. Each
Underwriter represents and warrants (but only with respect to itself) to the
Insurer as follows:

                  (a) Prospectus Supplement. It represents and warrants to and
agrees with the Insurer that the statements in the Prospectus Supplement made in
reliance upon and in conformity with written information relating to such
Underwriter furnished to Capital One Auto Finance, Inc. specifically for use in
the preparation of the Prospectus Supplement, and acknowledged in writing set
forth in the second paragraph (regarding concessions and discounts) and the
first sentence of the eighth paragraph (regarding marketmaking) under the
caption "Underwriting" in the Prospectus Supplement (referred to herein as the
"Underwriter Information"), are true and correct in all material respects.

                  (b) Corporate Power. It has the corporate power and authority
to execute and deliver this Agreement and the Underwriting Agreement and to
perform all of its obligations hereunder and thereunder in all material
respects.

                  (c) Authorization; Approvals. The execution, delivery and
performance of this Agreement and the Underwriting Agreement by such Underwriter
have been duly authorized by all necessary corporate proceedings. No further
approvals or filings of any kind, including, without limitation, any further
approvals of or further filing with any governmental agency or other
governmental authority, or any approval of such Underwriter's board of directors
or stockholders, are necessary for this Agreement and the Underwriting Agreement
to constitute the legal, valid and binding obligation of such Underwriter.

                  (d) Enforceability. This Agreement and the Underwriting
Agreement will each constitute a legal, valid and binding obligation of such
Underwriter, each enforceable in accordance with its terms, subject, as to the
enforcement of remedies, to bankruptcy, insolvency, reorganization, moratorium
and other similar laws affecting the enforceability of creditors' rights
generally applicable in the event of the bankruptcy, insolvency or
reorganization of such Underwriter and to general principles of equity.

                  (e) No Litigation. There are no actions, suits, proceedings or
investigations pending or, to the best of such Underwriter's knowledge,
threatened against it at law or in equity or before any court, governmental
agency, board or commission or any arbitrator which, if decided adversely, would
materially and adversely affect its condition (financial or otherwise) or its
operations or would materially and adversely affect its ability to perform its
obligations under this Agreement and the Underwriting Agreement.

         Section 4. [RESERVED].


                                       4
<PAGE>   6

         Section 5. INDEMNIFICATION.

                  (a) The Insurer hereby agrees, upon the terms and subject to
the conditions of this Agreement, to indemnify, defend and hold harmless each
Issuer Party and each Underwriter Party against (i) any and all Losses incurred
by them with respect to the offer and sale of any of the Offered Notes and
resulting from the Insurer's breach of any of its representations and warranties
set forth in Section 2 of this Agreement, and (ii) any and all Losses to which
any Issuer Party or any Underwriter Party may become subject, under the Act or
otherwise, subject to the limited scope of the Insurer Information described
below insofar as such Losses arise out of or result horn an untrue statement of
a material fact contained in the Prospectus Supplement or the omission to state
therein a material fact required to be stated therein or necessary to make the
statements therein not misleading, in each case to the extent, but only to the
extent, that such untrue statement or omission was made in the Insurer
Information included therein, and provided further, that it is understood that
the Insurer Information is limited and does not purport to provide the scope of
disclosure required to be included in a prospectus for a registrant under the
Securities Act of 1933, in connection with the public offer and sale of
securities of such registrant.

         (b) Each Underwriter hereby agrees, severally and not jointly, upon the
terms and subject to the conditions of this Agreement, to indemnify, defend and
hold harmless each Insurer Party against (i) any and all Losses incurred by it
with respect to the offer and sale of any of the Offered Notes and resulting
from such Underwriter's breach of any of its agreements, representations and
warranties set forth in Section 3 of this Agreement and (ii) any and all Losses
to which any Insurer Party may become subject, under the Act or otherwise,
insofar as such Losses arise out of or result from an untrue statement of a
material fact contained in the Prospectus Supplement or the omission to state
therein a material fact required to be stated therein or necessary to make the
statements therein not misleading in each case to the extent, but only to the
extent, that such untrue statement or omission was made in the Underwriter
Information (as defined above) included therein.

         (c) Upon the incurrence of any Losses entitled to indemnification
hereunder, the Indemnifying Party shall reimburse the Indemnified Party promptly
upon establishment by the Indemnified Party to the Indemnifying Party of the
Losses incurred.

         Section 6. NOTICE TO BE GIVEN.

                  (a) Except as provided in Section 7 below with respect to
contribution, the indemnification provided herein by the Indemnifying Party
shall be the exclusive remedy of each Indemnified Party for the Losses resulting
from the Indemnifying Party's breach of a representation, warranty or agreement
hereunder, provided, however, that each Indemnified Party shall be entitled to
pursue any other remedy at law or in equity for any such breach so long as the


                                       5
<PAGE>   7


damages sought to be recovered shall not exceed the Losses incurred thereby
resulting from such breach.

                  (b) In the event that any action or regulatory proceeding
shall be commenced or claim asserted which may entitle an Indemnified Party to
be indemnified under this Agreement, such party shall give the Indemnifying
Party written or facsimile notice of such action or claim reasonably promptly
after receipt of written notice thereof.

                  (c) Upon request of the Indemnified Party, the Indemnifying
Party shall retain counsel reasonably satisfactory to the Indemnified Party to
represent the Indemnified Party and any others the Indemnifying Party may
designate in such proceeding and shall pay the fees and disbursements of such
counsel related to such proceeding. The Indemnifying Party may, at its option,
at any time upon written notice to the Indemnified Party, assume the defense of
any proceeding and may designate counsel reasonably satisfactory to the
Indemnified Party in connection therewith, provided that the counsel so
designated would have no actual or potential conflict of interest in connection
with such representation. Unless it shall assume the defense of any proceeding,
the Indemnifying Party shall not be liable for any settlement of any proceeding,
effected without its written consent, but if settled with such consent or if
there be a final judgment for the plaintiff, the Indemnifying Party agrees to
indemnify the Indemnified Party from and against any loss or liability by reason
of such settlement or judgment. The Indemnifying Party shall be entitled to
participate in the defense of any such action or claim in reasonable cooperation
with, and with the reasonable cooperation of, each Indemnified Party.

                  (d) The Indemnified Party will have the right to employ its
own counsel in any such action, but the fees and expenses of such counsel will
be at the expense of such Indemnified Party unless (i) the employment of counsel
by the Indemnified Party at the Indemnifying Party's expense has been authorized
in writing by the Indemnifying Party, (ii) the Indemnifying Party has not in
fact employed counsel to assume the defense of such action within a reasonable
time after receiving notice of the commencement of the action or (iii) the named
parties to any such action include the Indemnifying Party on the one hand and,
on the other hand, the Indemnified Party, and representation of both parties by
the same counsel would be inappropriate due to actual or potential differing
interests between them (in which case if such Indemnified Party notifies the
Indemnifying Party in writing that it elects to employ separate counsel at the
expense of the Indemnifying Party, the Indemnifying Party shall not have the
right to assume the defense of such action or proceeding on such Indemnified
Party's behalf), in each of which cases the reasonable fees and expenses of
counsel (including local counsel) will be at the expense of the Indemnifying
Party, and all such fees and expenses will be reimbursed promptly as they are
incurred. In the event that any expenses so paid by the Indemnifying Party are
subsequently determined not to be required to be borne by the Indemnifying Party
hereunder, the party which received such payment shall promptly refund to the
Indemnifying Party the amount so paid by such Indemnifying Party.
Notwithstanding the foregoing, in connection with any one action or separate but
substantially similar or related actions in the same jurisdiction arising out of
the same general allegations or circumstances, the Indemnifying Party shall not
be liable for the fees and expenses of more than


                                       6
<PAGE>   8
one counsel for the Issuer Parties, more than one counsel for all Underwriter
Parties and more than one counsel for all Insurer Parties, as applicable.

                  (e) The Indemnified Parties shall cooperate with the
Indemnifying Parties in resolving any event, which would give rise to an
indemnity obligation pursuant to Section 5 hereof in the most efficient manner.

                  (f) No settlement of any such claim or action shall be entered
into without the consent of each Indemnified Party who is subject to such claim
or action, on the one hand, and each Indemnifying Party who is subject to such
claim or action, on the other hand, provided, however, that the consent of such
Indemnified Party shall not be required if such settlement fully discharges,
with prejudice against the plaintiff, the claim or action against such
Indemnified Party.

                  (g) Any failure by an Indemnified Party to comply with the
provisions of this Section shall relieve the Indemnifying Party of liability
only if such failure is materially prejudicial to any legal pleadings, grounds,
defenses or remedies in respect thereof or the Indemnifying Party's financial
liability hereunder, and then only to the extent of such prejudice.

         Section 7. CONTRIBUTION.

                  (a) To provide for just and equitable contribution if the
indemnification provided by the Insurer is determined to be unavailable for any
Underwriter Party (other than pursuant to Section 4 or 5 of this Agreement), or
if the indemnification provided by the Underwriters is determined to be
unavailable for any Insurer Party (other than pursuant to Section 4 or 6 of this
Agreement), the Insurer and the relevant Underwriter shall contribute to the
aggregate costs of liabilities arising from any breach of their respective
representations and warranties set forth in this Agreement on the basis of the
relative fault of all Insurer Parties and all relevant Underwriter Parties.

                  (b) To provide for just and equitable contribution if the
indemnification provided by the Insurer is determined to be unavailable for the
Issuer Parties (other than pursuant to Section 5 or 6 of this Agreement), the
Insurer shall contribute to the aggregate cost of liabilities arising from any
breach of their respective representations and warranties set forth in this
Agreement on the basis of the relative fault of all Insurer Parties and the
Issuer Parties.

                  (c) Notwithstanding anything in this Section 7 to the
contrary, (i) the Insurer shall not be requited to contribute an amount in
excess of the amount by which the total of the insurance premiums that have been
received by the Insurer under the Insurance Agreement exceeds the amount of any
damages that the Insurer has otherwise been required to pay in respect of any
bleach by the Insurer of the representations and warranties contained in Section
2 hereof, and (ii) no Underwriter shall be required to contribute an amount in
excess of the amount by which the total underwriting fees, discounts and
commissions received by such Underwriter exceeds the amount of any damages that
such Underwriter has otherwise been required to pay in


                                       7
<PAGE>   9


respect of any breach by such Underwriter of its representations and warranties
contained in Section 3 hereof.

                  (d) The relative fault of each Indemnifying Party, on the one
hand, and of each Indemnified Party, on the other hand, shall be determined by
reference to, among other things, whether the breach of, or alleged breach of,
any of its representations and warranties set forth in Section 2 or 3 of this
Agreement relates to information supplied by, or action within the control of,
the Insurer Party or the relevant Underwriter Party and the Parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such breach.

                  (e) The Parties agree that the Insurer shall be solely
responsible for the Insurer Information and for the Insurer Financial
Statements, that each Underwriter shall be responsible for the Underwriter
Information provided by such Underwriter in writing for use in the Prospectus
Supplement.

                  (f) No person guilty of fraudulent misrepresentation (within
the meaning of Section 11(f) of the Act) shall be entitled to contribution from
any person who was not guilty of such fraudulent misrepresentation.

                  (g) The indemnity agreements contained in this Agreement shall
remain operative and in full force and effect, regardless of (i) any
investigation made by or on behalf of any Underwriter Party, any Insurer Party
or any Issuer Party, (ii) the issuance of any Offered Notes or the Policy or
(iii) any termination of this Agreement.

                  (h) Upon the incurrence of any Losses entitled to contribution
hereunder, the contributor shall reimburse the party entitled to contribution
promptly upon establishment by the party entitled to contribution to the
contributor of the Losses incurred.

                  (i) The Underwriters shall be severally and not jointly liable
for any contribution required by this Section 7.

         Section 8. NOTICES. All notices and other communications provided for
under this Agreement shall be addressed to the address set forth below as to
each party or at such other address as shall be designated by a party in a
written notice to the other party.

         If to the Insurer:  MBIA Insurance Corporation
                             113 King Street
                             Armonk, NY 10504
                             Attention: Insured Portfolio Management--Structured
                             Finance (IPM-SF)


                                       8
<PAGE>   10

         If to the Issuer Parties:

                               Capital One Auto Finance, Inc.
                               8000 Jones Branch Drive
                               McLean, Virginia 22202
                               Facsimile: (703) 875-1389
                               Confirmation: (703) 875-1305

                               With a copy to Legal Department
                               Facsimile: (703) 875-1589
                               Confirmation: (703) 875-1000

                               Capital One Auto Receivables, LLC
                               8000 Jones Branch Drive
                               McLean, Virginia 22202
                               Facsimile: (703) 875-1389
                               Confirmation: (703) 875-1305

                               With a copy to Legal Department
                               Facsimile: (703) 875-1589
                               Confirmation: (703) 875-1000

         If to the Representative:

                               Banc of America Securities LLC
                               100 North Tryon Street, 10th Floor
                               NC1-007-11-07
                               Charlotte, NC 28255
                               Attention: Andy Glenn

         Section 9. GOVERNING LAW, ETC. This Agreement shall be deemed to be a
contract under the laws of the State of New York and shall be governed by and
construed in accordance with the laws of the State of New York without regard to
its conflicts of laws provisions. This Agreement may not be assigned by any
party without the express written consent of each other party. Amendments of
this Agreement shall be in writing signed by each party. This Agreement shall
not be effective until executed by each of the Insurer, each Issuer Party and
the Underwriters.

         Section 10. OTHER OBLIGATIONS NOT EFFECTED. This Agreement in no way
limits or otherwise affects the indemnification obligations of the Underwriters
and COAF under the Underwriting Agreement.

         Section 11. LIMITATIONS. Nothing in this Agreement shall be construed
as a representation or undertaking by the Insurer concerning maintenance of the
rating currently assigned to its claims-paying ability by Moody's Investors
Service, Inc. ("Moody's") and/or Standard & Poor's, a division of The
McGraw-Hill Companies, Inc. ("S&P") or any other rating agency (collectively,
the "Rating Agencies").


                                       9
<PAGE>   11


         Section 12. COUNTERPARTS. This Agreement may be executed in any number
of counterparts, each of which shall together constitute but one and the same
instrument.

         Section 13. NON-PETITION. So long as the Insurance Agreement is in
effect, and for one year following its termination, each of the parties hereto
agree that it (with respect to itself) file any involuntary petition or
otherwise institute any bankruptcy, reorganization, arrangement, insolvency or
liquidation proceeding or other proceeding under any federal or state bankruptcy
or similar law against the Issuer Parties or the Seller.


                                       10
<PAGE>   12


         IN WITNESS WHEREOF, the Parties hereto have caused this Indemnification
Agreement to be duly executed and delivered by their respective officers
thereunto duly authorized, all as of the date first above written.

                                MBIA INSURANCE CORPORATION

                                By  /s/ LISA WILSON
                                  ----------------------------------------------
                                Title   Assistant Secretary
                                     -------------------------------------------


                                BANC OF AMERICA SECURITIES LLC, for
                                itself and as Representative of the Underwriters

                                By /s/ JAMES G. MACKEY
                                  ----------------------------------------------
                                Title   Vice President
                                     -------------------------------------------


                                CAPITAL ONE AUTO FINANCE, INC., as Issuer
                                Party

                                By /s/ JEFFERY ELSWICK
                                  ----------------------------------------------
                                Title  Manager of Securitization
                                     -------------------------------------------


                                CAPITAL ONE AUTO RECEIVABLES, LLC, as
                                Issuer Party

                                By /s/ JEFFERY ELSWICK
                                  ----------------------------------------------
                                Title  President
                                     -------------------------------------------










<PAGE>   13

                               TABLE OF CONTENTS

Section 1.    Definitions......................................................1
Section 2.    Representations and Warranties of the Issuer.....................2
Section 3.    Representations and Warranties of the Underwriters...............4
Section 4.    [RESERVED].......................................................4
Section 5.    Indemnification..................................................5
Section 6.    Notice to be Given...............................................5
Section 7.    Contribution.....................................................7
Section 8.    Notices..........................................................8
Section 9.    Governing Law, Etc. .............................................9
Section 10.   Other Obligations Not Effected...................................9
Section 11.   Limitations......................................................9
Section 12.   Counterparts.....................................................9
Section 13.   Non-petition.....................................................9


TESTIMONIUM.......................................................SIGNATURE PAGE
SIGNATURES........................................................SIGNATURE PAGE