<PAGE>

                                                                    EXHIBIT 10.5

                       FIRST AMENDMENT TO CREDIT AGREEMENT

         This First Amendment to Credit Agreement (this "FIRST AMENDMENT") is
executed as of October 31, 2002 (the "EFFECTIVE DATE"), by and among Encore
Acquisition Company, a Delaware corporation ("BORROWER"), Encore Operating,
L.P., a Texas limited partnership ("OPERATING"), Fleet National Bank, a national
banking association, as Administrative Agent ("ADMINISTRATIVE AGENT"), and the
financial institutions a party hereto as Banks ("BANKS").

                                   WITNESSETH:

         WHEREAS, Borrower, Operating, Administrative Agent, the other Agents a
party thereto and Banks are parties to that certain Credit Agreement dated as of
June 25, 2002 (the "CREDIT AGREEMENT") (unless otherwise defined herein, all
terms used herein with their initial letter capitalized shall have the meaning
given such terms in the Credit Agreement); and

         WHEREAS, pursuant to the Credit Agreement, Banks have made a revolving
credit loan to Borrower; and

         WHEREAS, Borrower and Operating have requested that Banks (a) amend
certain terms of the Credit Agreement in certain respects, and (b) reaffirm the
Borrowing Base of $220,000,000 to be effective as of December 1, 2002 and
continuing until the first Redetermination thereafter; and

         WHEREAS, subject to the terms and conditions set forth herein, Banks
have agreed to Borrower's and Operating's requests.

         NOW THEREFORE, for and in consideration of the mutual covenants and
agreements herein contained and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged and confessed,
Borrower, Operating, Administrative Agent and each Bank hereby agree as follows:

         SECTION 1. AMENDMENTS. In reliance on the representations, warranties,
covenants and agreements contained in this First Amendment, and subject to the
satisfaction of the conditions precedent set forth in Section 3 hereof, the
Credit Agreement is hereby amended effective as of the Effective Date in the
manner provided in this Section 1.

         1.1.     AMENDMENT TO DEFINITIONS. The definitions of "LOAN PAPERS" and
"PERMITTED ENCUMBRANCES" contained in Section 1.1 of the Credit Agreement shall
be amended to read in full as follows:

                  "LOAN PAPERS" means this Agreement, the First Amendment, the
         Notes, the Mortgages, each Borrower Pledge Agreement, each Subsidiary
         Pledge Agreement, each Facility Guaranty, and all other certificates,
         documents or instruments delivered in connection with this Agreement,
         as the foregoing may be amended from time to time.

                  "PERMITTED ENCUMBRANCES" means with respect to any asset:

                                       1

<PAGE>

         (a)      Liens (if any) securing the Obligations (including, without
limitation, indebtedness, liabilities and obligations pursuant to any Hedge
Transaction entered into by a Credit Party with any Bank or any Affiliate of any
Bank);

         (b)      minor defects in title which do not secure the payment of
money and otherwise have no material adverse effect on the value or the
operation of the subject property, and for the purposes of this Agreement, a
minor defect in title shall include, but not be limited to, easements, zoning
restrictions, rights-of-way, servitudes, permits, surface leases and other
similar rights in respect of surface operations, and easements for pipelines,
streets, alleys, highways, telephone lines, power lines, railways and other
easements and rights-of-way, on, over or in respect of any of the properties of
any Credit Party that are customarily granted in the oil and gas industry;

         (c)      contractual or statutory Liens securing obligations for labor,
services, materials and supplies furnished to Mineral Interests and Liens
arising under joint operating agreements entered into in the ordinary course of
business, in each case securing obligations which are not delinquent (except to
the extent permitted by Section 9.7);

         (d)      contractual or statutory mechanic's, materialmen's,
warehouseman's, journeyman's and carrier's Liens and other similar Liens arising
in the ordinary course of business which are not delinquent (except to the
extent permitted by Section 9.7);

         (e)      Liens for Taxes or assessments not yet due or not yet
delinquent, or, if delinquent, that are not required to be paid subject to
satisfaction of the conditions set forth in Section 9.7;

         (f)      lease burdens payable to third parties which are deducted in
the calculation of discounted present value in the Reserve Report including,
without limitation, any royalty, overriding royalty, net profits interest,
production payment, carried interest or reversionary working interest;

         (g)      Liens encumbering assets securing Debt incurred to finance the
purchase of such assets, provided, that (i) the principal amount of the Debt
secured by a purchased asset shall not exceed one hundred percent (100%) of the
purchase price of such asset, (ii) such Liens shall not extend to or encumber
any other asset of any Credit Party, (iii) such Liens shall attach to such
purchased asset substantially simultaneously with the purchase of such asset,
and (iv) the aggregate amount of all Debt secured by such Liens shall not exceed
$15,000,000;

         (h)      Liens securing Hedge Transactions, including, without
limitation, pledges of cash or cash equivalents, provided, that, (i) such Hedge
Transactions comply with Section 10.11 to the extent applicable, and (ii) the
aggregate amount of cash or cash equivalents pledged (or the fair market value
of other, non-cash collateral pledged) shall not exceed $10,000,000 at any time;
and

         (i)      to the extent not included in clauses (a) through (h) above,
Permitted Encumbrances under and as defined in the Mortgages.

                                       2

<PAGE>

         1.2.     DEBT COVENANT. Section 10.1 of the Credit Agreement shall be
amended to read in full as follows:

         "Section 10.1 INCURRENCE OF DEBT. Borrower and Operating will not, nor
         will Borrower and/or Operating permit any other Credit Party to, incur,
         become or remain liable for any Debt other than (a) the Obligations
         (including, without limitation, Debt pursuant to any Hedge Transaction
         entered into by a Credit Party with a Bank or any Affiliate of any
         Bank), (b) the Permitted Subordinate Debt, (c) other Debt under Hedge
         Transactions, provided, that such Hedge Transactions comply with the
         terms and provisions of this Agreement, including, without limitation,
         Section 10.11, and (d) other Debt in an aggregate amount outstanding at
         any time not to exceed $15,000,000."

         1.3.     USE OF PROCEEDS COVENANTS. Section 10.7 of the Credit
Agreement shall be amended by deleting the last sentence thereof, and in lieu
thereof, substituting the following sentence:

         "Without limiting the foregoing, no Letter of Credit will be issued
         hereunder for the purpose of providing credit enhancement with respect
         to any Debt or equity security of any Credit Party, or to secure any
         Credit Party's obligations with respect to Hedge Transactions other
         than (i) Hedge Transactions with a Bank or an Affiliate of such Bank,
         or (ii) Hedge Transactions with a counterparty other than a Bank or an
         Affiliate of a Bank provided that such Hedge Transactions otherwise
         comply with the terms and provisions of this Agreement, including,
         without limitation, Section 10.1 and Section 10.11.

         SECTION 2. BORROWING BASE. The Borrowing Base shall continue to be
$220,000,000 from December 1, 2002 and continuing until the first
Redetermination thereafter. Borrower, Operating and Banks agree that the
Redetermination provided for in this Section 2 (a) shall be deemed to be the
Scheduled Redetermination to occur on December 1, 2002 pursuant to Section 5.2
of the Credit Agreement, and (b) shall not be construed or deemed to be a
Special Redetermination for purposes of Section 5.3 of the Credit Agreement.

         SECTION 3. CONDITIONS PRECEDENT. The effectiveness of the amendments to
the Credit Agreement contained in Section 1 hereof is subject to the
satisfaction of each of the following conditions precedent:

         3.1.     NO DEFAULT. No Default or Event of Default shall have occurred
which is continuing.

         3.2.     FEES. Borrower shall have paid to Administrative Agent any
fees payable to Administrative Agent or any Affiliate of Administrative Agent
pursuant to this First Amendment and any separate agreement among Borrower,
Operating, Administrative Agent or any Affiliate of Administrative Agent in
consideration for providing services in connection with the credit facilities
provided by the Credit Agreement.

         3.3.     OTHER DOCUMENTS. Administrative Agent shall have been provided
with such other documents, instruments and agreements, and Borrower and
Operating shall have taken such actions, as Administrative Agent may reasonably
require in connection with this First Amendment and the transactions
contemplated hereby.

                                       3
<PAGE>

         SECTION 4. REPRESENTATIONS AND WARRANTIES OF BORROWER AND OPERATING. TO
induce Banks and Administrative Agent to enter into this First Amendment,
Borrower and Operating hereby jointly and severally represent and warrant to
Banks and Administrative Agent as follows:

         4.1.     REAFFIRM EXISTING REPRESENTATIONS AND WARRANTIES. Each
representation and warranty of each Credit Party contained in the Credit
Agreement and the other Loan Papers is true and correct on the date hereof and
will be true and correct after giving effect to the amendments set forth in
Section 1 hereof.

         4.2.     DUE AUTHORIZATION; NO CONFLICT. The execution, delivery and
performance by Borrower and Operating of this First Amendment are within
Borrower's and Operating's corporate and partnership powers (as applicable),
have been duly authorized by all necessary action, require no action by or in
respect of, or filing with, any governmental body, agency or official and do not
violate or constitute a default under any provision of applicable law or any
Material Agreement binding upon Borrower, Operating or any other Credit Party or
result in the creation or imposition of any Lien upon any of the assets of any
Credit Party except Permitted Encumbrances.

         4.3.     VALIDITY AND ENFORCEABILITY; EXTENSION OF LIENS. This First
Amendment constitutes the valid and binding obligation of Borrower and Operating
enforceable in accordance with its terms, except as (i) the enforceability
thereof may be limited by bankruptcy, insolvency or similar laws affecting
creditor's rights generally, and (ii) the availability of equitable remedies may
be limited by equitable principles of general application.

         4.4.     NO DEFAULT OR EVENT OF DEFAULT. No Default or Event of Default
has occurred which is continuing.

         SECTION 5. MISCELLANEOUS.

         5.1.     REAFFIRMATION OF LOAN PAPERS. Any and all of the terms and
provisions of the Credit Agreement and the Loan Papers shall, except as amended
and modified hereby, remain in full force and effect. The amendments
contemplated hereby shall not limit or impair any Liens securing the
Obligations, each of which are hereby ratified, affirmed and extended to secure
the Obligations as they may be modified pursuant hereto.

         5.2.     PARTIES IN INTEREST. All of the terms and provisions of this
First Amendment shall bind and inure to the benefit of the parties hereto and
their respective successors and assigns.

         5.3.     LEGAL EXPENSES. Borrower hereby agrees to pay on demand all
reasonable fees and expenses of counsel to Administrative Agent incurred by
Administrative Agent in connection with the preparation, negotiation and
execution of this First Amendment and all related documents.

         5.4.     COUNTERPARTS. This First Amendment may be executed in
counterparts, and all parties need not execute the same counterpart; however, no
party shall be bound by this First Amendment until Borrower, Operating and
Required Banks have executed a counterpart. Facsimiles shall be effective as
originals.

                                       4

<PAGE>

         5.5.     COMPLETE AGREEMENT. THIS FIRST AMENDMENT, THE CREDIT AGREEMENT
AND THE OTHER LOAN PAPERS REPRESENT THE FINAL AGREEMENT AMONG THE PARTIES AND
MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR ORAL AGREEMENTS
OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN OR AMONG THE
PARTIES.

         5.6.     HEADINGS. The headings, captions and arrangements used in this
First Amendment are, unless specified otherwise, for convenience only and shall
not be deemed to limit, amplify or modify the terms of this First Amendment, nor
affect the meaning thereof.

         5.7.     EFFECTIVENESS. This First Amendment shall be effective
automatically and without necessity of any further action by Borrower,
Operating, Administrative Agent or Banks when counterparts hereof have been
executed by Borrower, Operating and Required Banks, and all conditions to the
effectiveness hereof set forth herein have been satisfied.

         IN WITNESS WHEREOF, the parties hereto have caused this First Amendment
to be duly executed by their respective Authorized Officers on the date and year
first above written.

                           [Signature pages to follow]

                                       5

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

BORROWER:

ENCORE ACQUISITION COMPANY,
a Delaware corporation

By: /s/ MORRIS B SMITH
    --------------------------------
Name: MORRIS B  SMITH
Title: EJP - CFO

OPERATING:

ENCORE OPERATING, L.P.,
a Texas limited partnership

By: EAP Operating, Inc.,
    a Delaware corporation,
    its sole general partner

    By: /s/ MORRIS B SMITH
        -----------------------------------
    Name: MORRIS B SMITH
    Title: EJP - CFO

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
            FIRST AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT
                                  BY AND AMONG
                              HYPERION ENERGY, LP,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

ADMINISTRATIVE AGENT:

FLEET NATIONAL BANK,
as Administrative Agent

By: /s/ Jeffrey H. Rathkamp
    -------------------------------
    Jeffrey H. Rathkamp,
    Vice President

BANKS:

FLEET NATIONAL BANK,
as a Bank

BY: /s/ Jeffrey H. Rathkamp
   ------------------------------------
   Jeffrey H. Rathkamp,
   Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO

BANK:

WACHOVIA BANK, N.A.

By: /s/ David E. Humphreys
    -------------------------------
Name: David E. Humphreys
Title: Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

BANK:

FORTIS CAPITAL CORP.

BY: /s/ David Montgomery
    -----------------------------------
NAME: David Montgomery
Title: Senior Vice President

By /s/ Darrell W. Holley
   ---------------------------------------
Name: Darrell W. Holley
Title: Managing Director

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO

BANK:

BNP PARIBAS

By: /s/ David Dodd
   ----------------------------
Name: David Dodd
Title: Director

By: /s/ Betsy Jocher
   -------------------------------
Name: Betsy Jocher
TITLE: Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO

BANK:

CREDIT SUISSE FIRST BOSTON,
CAYMAN ISLANDS BRANCH

By: /s/ James P. Moran
   -----------------------------------
Name: JAMES P. MORAN
Title: DIRECTOR

By: /s/ Ian W. Nalitt
   -------------------------------------
Name: IAN W. NALITT
Title: ASSOCIATE

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

BANK:

THE FROST NATIONAL BANK

By: /s/ John S. Warren
   ------------------------------------
Name: John S. Warren
TITLE: Senior Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

BANK:

UNION BANK OF CALIFORNIA, N.A.

By: /s/ Gary Shekerjian
    ------------------------------
Name: Gary Shekerjian
Title:   Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO

BANK:

COMERICA BANK - TEXAS

By: /s/ Michele Jones
    ----------------------------------
Name: Michele Jones
Title: Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO

BANK:

COMPASS BANK

By: /s/ Dorothy Marchand
   ------------------------------
Name: Dorothy Marchand
Title: Senior Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

BANK:

SUNTRUST BANK

By: /s/ Ilene S. Fowler
    ----------------------------
Name: Ilene S. Fowler
Title:  Director

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO

BANK:

RZB FINANCE LLC

By: /s/ Pearl Geffers
    ---------------------------------
Name: PEARL GEFFERS
Title:  FIRST VICE PRESIDENT

By: /s/ John A. Valiska
   ----------------------------------
Name: John A. Valiska
Title: Group Vice President

                                [Signature Page]

<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       FIRST AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                         AND THE BANKS A PARTY THERETO

BANK:

BANK OF SCOTLAND

By: /s/ Joseph Fratus
    ----------------------------------
Name: JOSEPH FRATUS
TITLE: FIRST VICE PRESIDENT

                                [Signature Page]