<PAGE>   1
                                                                   EXHIBIT 10.5






                ASSIGNMENT, ACKNOWLEDGMENT, AGREEMENT AND WAIVER

         THIS Assignment, Acknowledgment, and Waiver (this "Agreement") dated
as of the 31st day of March, 2000, is among the persons listed as equity
investors on the signature pages hereof, (each an "Equity Investor" and
collectively the "Equity Investors"); BARGO ENERGY COMPANY, a Texas corporation
("Issuer") and CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, as administrative
agent (in such capacity, the "Administrative Agent") for those Lenders
("Lenders") listed on Annex I attached hereto with Agent acting in such
capacity on behalf of such Lenders pursuant to the document also described on
Annex I (the Equity Investors, Issuer and Administrative Agent collectively
being hereinafter collectively called the "Parties"),

                              W I T N E S S E T H:

         WHEREAS, the Equity Investors have severally agreed pursuant to a
Subscription Agreement dated as of March 31, 2000, between the Issuer and each
Equity Investor (as the same may from time to time be amended, renewed,
supplemented or otherwise modified, the "Subscription Agreement") to purchase
shares of Preferred Stock and, at the election of the Equity Investor, Common
Stock or Warrants (collectively, the "Securities"), from the Issuer through
payment of the Equity Investor's share of the aggregate purchase price
("Purchase Price"), as set forth in the Subscription Agreement; and

         WHEREAS, in the Subscription Agreement the Equity Investors have
committed to purchase the Securities for an aggregate Purchase Price of
$22,500,000 and have the right and option to purchase up to an aggregate of
$45,000,000 of the Securities; and

         WHEREAS, Issuer has borrowed $22,500,000 from the Lenders under
Tranche A Term Loans (as defined in the Credit Agreement, dated as of March 31,
2000 among Issuer, Administrative Agent and the other lenders party thereto
("Credit Agreement")), evidenced by the Tranche A Term Notes (as defined in the
Credit Agreement); and

         WHEREAS, to induce the Lenders to make the Tranche A Term Loans,
Issuer has agreed to assign its rights under the Subscription Agreement to the
Administrative Agent on behalf of the Lenders, to enter into an escrow
arrangement ("Escrow") with the Administrative Agent and the Equity Investors
into which certificates and other documents representing the Securities, and
related agreements, shall be placed, with the Administrative Agent acting as
the escrow agent (in such capacity, the "Escrow Agent") as further described
below; and


         WHEREAS, the Equity Investors have agreed to acknowledge and agree to
the aforementioned assignment, to enter into the Escrow with the Issuer, the
Administrative Agent and the Escrow Agent in order to fund their subscription
pursuant to the Subscription Agreement and in order to carry out the intentions
of this Agreement; and




<PAGE>   2





         WHEREAS, the Equity Investors desire to waive any defenses they may
have against the Issuer with respect to the payment by them of their respective
Purchase Price other than satisfaction of the conditions to their respective
obligations set forth in Section 4.6 of the Subscription Agreement, and
recognize the Administrative Agent as a third-party beneficiary of the
Subscription Agreement;

         NOW, THEREFORE, in consideration of the premises and the agreements,
provisions and covenants herein contained, the Parties hereby agree as follows:

                                   SECTION  1
                      ASSIGNMENT OF SUBSCRIPTION AGREEMENT

         1.1      Assignment. Issuer, for good and valuable consideration, the
receipt of which is hereby acknowledged, hereby GRANTS, TRANSFERS and ASSIGNS
to the Agent for the benefit of the Lenders all of its rights, titles, and
interests in and to and arising from the Subscription Agreement, and any and
all other contracts or agreements, whether now or hereafter existing relating
to the purchase of the Securities by any Equity Investor, together with all
revenues, monies, proceeds, benefits, and payments due and to become due the
Issuer and accruing and to accrue unto the Issuer under and by virtue of the
Subscription Agreement, or any such other contract or agreement, and any and
all amendments and renewals thereof and supplements thereto.

                                    SECTION 2
              REPRESENTATIONS, WARRANTIES, AND COVENANTS OF ISSUER

         2.1      Representations and Warranties. The Issuer represents and
warrants, now and continuing throughout the term of this Agreement (which
representations and warranties will survive the delivery of this Agreement)
that:

                  (a)      the Issuer is the sole owner of its interests in the
                           Subscription Agreement;

                  (b)      the Subscription Agreement is valid and enforceable
                           and has not been altered, modified or amended in any
                           manner whatsoever save as herein set forth;

                  (c)      neither the Issuer nor the Equity Investors are in
                           default under any of the terms, covenants or
                           conditions thereof;

                  (d)      the Issuer's interest under the Subscription
                           Agreement is assignable pursuant to the terms
                           hereof; and

                  (e)      the Subscription Agreement commits the Equity
                           Investors to purchase Securities for an aggregate
                           Purchase Price of $22,500,000 and grants the



<PAGE>   3



                           Equity Investors the right and option to purchase
                           additional Securities for an aggregate Purchase
                           Price of $45,000,000.

         2.2      Covenants and Agreements of Issuer. The Issuer covenants and
                  agrees with the Administrative Agent:

                  (a)      to observe and perform all the obligations imposed
                           upon it under the Subscription Agreement and not to
                           do or permit to be done anything to impair the
                           security thereof;

                  (b)      not to execute any other assignment of its interests
                           in the Subscription Agreement;

                  (c)      not to alter, amend, modify or otherwise change the
                           terms of the Subscription Agreement without the prior
                           written consent of the Administrative Agent, or
                           cancel or terminate the Subscription Agreement or
                           accept a surrender thereof, or pledge, convey or
                           otherwise transfer or suffer or permit a pledge,
                           conveyance or other transfer of the Securities or of
                           any interest therein so as to effect directly or
                           indirectly, proximately or remotely, a cancellation,
                           termination or diminution of the obligations of the
                           Equity Investors thereunder;

                  (d)      to execute and deliver, and to require the Equity
                           Investors to execute and deliver, at the request of
                           the Administrative Agent, all such further
                           assurances, acknowledgments and certificates for the
                           purposes hereof as the Administrative Agent shall
                           from time to time require; and

                  (e)      that if the Issuer shall receive or become entitled
                           to receive any payments or other sums (whether paid
                           in cash or other property), distributions or payments
                           of any kind or description with respect to or on
                           account of the Subscription Agreement, to accept same
                           as agent for the Administrative Agent, to hold same
                           in trust for the Administrative Agent, and to
                           forthwith deliver same to the Administrative Agent in
                           the form received, with the endorsement of the Issuer
                           when necessary, to be applied by the Administrative
                           Agent pursuant to Section 6.


<PAGE>   4




                                    SECTION 3
          ACKNOWLEDGMENT, COVENANTS AND AGREEMENT OF EQUITY INVESTORS

         3.1      Acknowledgment. Each of the Equity Investors acknowledges the
assignment by the Issuer of its rights, titles, and interests in and to the
Subscription Agreement pursuant to Section 1 above.

         3.2      Covenants and Agreements of Equity Investors. Each Equity
Investor covenants and agrees with the Administrative Agent:

                  (a)      following receipt by Equity Investor of the Purchase
                           Notice (as defined in the Subscription Agreement) in
                           accordance with the Subscription Agreement and
                           provided (i) the Expiration Date (as defined in the
                           Subscription Agreement) has not occurred and (ii) the
                           conditions precedent to the Equity Investor's
                           obligations under the Subscription Agreement set
                           forth in Section 4.6 have been satisfied, to pay such
                           Equity Investor's Purchase Price as provided in the
                           Subscription Agreement into the Escrow with the
                           Escrow Agent on or before the Closing Date;

                  (b)      to observe and perform all the obligations imposed
                           upon it under its Subscription Agreement and not to
                           do or permit to be done anything to impair the
                           security thereof;

                  (c)      not to alter, amend, modify or otherwise change the
                           terms of the Subscription Agreement without the prior
                           written consent of the Administrative Agent, or
                           cancel or terminate the Subscription Agreement or
                           accept a surrender thereof, or pledge, convey or
                           otherwise transfer or suffer or permit a pledge,
                           conveyance or other transfer of its rights in and to
                           the Securities or any interest therein so as to
                           effect, directly or indirectly, proximately or
                           remotely, a cancellation, termination, or diminution
                           of the obligations of the Issuer thereunder; and

                  (d)      to execute and deliver at the request of the
                           Administrative Agent all such further assurances,
                           acknowledgments and certificates for the purposes
                           hereof as the Administrative Agent shall from time
                           to time reasonably require.

         3.3      Notices to Administrative Agent. Each Equity Investor
acknowledges that the Administrative Agent may act for and on behalf of the
Issuer under the Subscription Agreement. Upon receipt of a Purchase Notice,
each Equity Investor will cause copies of all notices or requests required or
permitted under the Subscription Agreement, including an Election to Receive
Warrants contemplated by Section 2.5 of the Subscription Agreement, to be
delivered to the Administrative Agent at the same time as such notices or
requests are delivered to the Issuer.


<PAGE>   5





                                    SECTION 4
                       AGREEMENTS OF ADMINISTRATIVE AGENT

         4.1      Withdrawal from Escrow; Delivery to Equity Investors. If,
prior to the Expiration Date, the Tranche A Equity Subscription Date (as
defined in the Credit Agreement) occurs and the Tranche A Loan has not been
repaid in full, the Administrative Agent may, and, at the request of the
Company shall, deliver a certificate executed by an officer of the
Administrative Agent to the Escrow Agent as contemplated by Section 4(a) of the
Escrow Agreement stating that the Tranche A Equity Subscription Date has
occurred and that amounts remain outstanding on the Tranche A Loan, and
withdraw from Escrow the Purchase Notices. The Administrative Agent shall
complete the blanks in the Purchase Notice by filling in the aggregate Purchase
Price, the Total Number of Units, the Investor's Share of Units, the number of
shares of Common Stock to be purchased by the Equity Investor, the Closing Date
and the wire transfer instructions for payment of the Purchase Price, all in
accordance with the terms of the Subscription Agreement. The Administrative
Agent shall promptly deliver a Purchase Notice to each Equity Investor as
provided in the Subscription Agreement. Notwithstanding anything set forth
herein, no Equity Investor shall have an obligation to purchase Units if the
Purchase Notice is not delivered to the Equity Investor prior to the Expiration
Date, as defined in the Subscription Agreement.

         4.2      Actions on the Closing Date. On the Closing Date (as defined
in the Subscription Agreement), the Administrative Agent shall deliver a
certificate executed by an officer of the Administrative Agent setting for the
number of shares of Preferred Stock and Common Stock or Warrants (based on
copies of the Election to Receive Warrants received by the Administrative
Agent) being purchased by each Equity Investor, and directing the Escrow Agent
to deliver such securities to the Equity Investor upon receipt of the Purchase
Price payable by the Equity Investor.

         4.3      Release. Upon the earlier of payment in full of the Tranche A
Term Loan or if Purchase Notices have not been delivered to the Equity
Investors, the Expiration Date (as defined in the Subscription Agreement), the
Administrative Agent shall withdraw the Escrowed Items from the Escrow and
promptly return them to the Issuer, and shall assign any rights it may have
under the Subscription Agreement to the Issuer.

                                   SECTION 5
                                     ESCROW

         5.1      Escrow Agreement. The parties hereto agree to enter into the
Escrow Agreement in the form thereof attached hereto as Exhibit A.

         5.2      Escrow Items. Issuer has placed into Escrow and delivered to
the Escrow Agent the Escrow Items (other than the Purchase Price) as defined in
the Escrow Agreement.

         5.3      No Retention. The holding of the Preferred Stock by the
Escrow Agent pursuant to the Escrow Agreement shall not be deemed a retention
by the Administrative Agent or the Lenders in satisfaction of the Indebtedness.



<PAGE>   6





                                    SECTION 6
                                PAYMENT ON NOTES

         6.1      Payments. The Agent hereby agrees that upon receipt of the
Purchase Price for Securities from the Escrow Agent, the Agent will apply such
funds toward repayment of the Tranche A Term Loan Notes corresponding to such
Purchase Price (and the Tranche B Term Loan Notes, under the circumstances
provided in Section 2.4 of the Subscription Agreement).



                                    SECTION 7
                RIGHTS, DUTIES AND POWERS OF ADMINISTRATIVE AGENT

         7.1      Rights and Powers. The Issuer does hereby irrevocably
authorize and empower the Administrative Agent to do the following, by and on
behalf of the Issuer, in the Issuer's name, place and stead: (a) demand,
receipt for and receive all sums of money to which this Agreement relates; (b)
commence, maintain or discontinue any action, suit or other proceeding which it
deems advisable to collect or enforce the payment of the sums, monies,
benefits, revenues, proceeds and payments assigned hereby; (c) to endorse in
the name of the Issuer any checks, drafts or other instruments payable to the
Issuer or to its order, as may be issued in whole or in partial payment in
connection with the Subscription Agreement; (d) to deliver the Purchase Notice,
Preferred Stock Certificates and Warrants to the Equity Investors, to receive
the Purchase Price from the Equity Investors, to deliver the Transfer Agent
Instructions to the Issuer's transfer agent and to otherwise take such actions
as the Administrative Agent shall deem appropriate hereunder and under the
Subscription Agreement to deliver the Securities in exchange for the Purchase
Price; and (e) to fill in the blanks in the Escrow Items as provided in the
Subscription Agreement and Article 4.

         7.2      Failure to Collect or Receive Money. Failure of the
Administrative Agent to collect or receive any sums of money to which it might
be entitled to hereunder, or failure to take any action to collect any sums
shall not in anywise prejudice, release or relinquish any of the rights of the
Administrative Agent hereunder.

         7.3      No Duty to Act. Except as provided in Sections 4.2 and 4.3,
the Administrative Agent shall not be under any duty or obligation to take any
action, bring any suit or act in any regard in order to enforce the collection
of any or all of the monies assigned hereunder; and, although it has the right
to do so, failure on the part of the Administrative Agent to do so shall not
relieve, diminish or affect the rights hereunder given or the monies hereby
assigned.

         7.4      Third-Party Beneficiary. The Issuer and each Equity Investor
hereby agree that the Administrative Agent is and shall be a third-party
beneficiary of the Subscription Agreement, and each of them hereby further
agrees and covenants to execute any and all other instruments or documents
necessary to name the Administrative Agent as a third-party beneficiary of the
Subscription Agreement.



<PAGE>   7




                                    SECTION 8
                                  MISCELLANEOUS

         8.1      Agreement Irrevocable. This Agreement may not be revoked by
the Issuer or any Equity Investor and shall continue to be effective with
respect to debt under the Tranche A Term Loans and Tranche B Term Loan arising
or created after any attempted revocation by the Issuer and/or any Equity
Investor. This Agreement shall remain in full force and effect until the
earlier to occur of (a) full and final payment of the Tranche A Term Loans is
made and (b) if Purchase Notices have not been delivered as provided in the
Subscription Agreement, the Expiration Date. 8.2 Issuer's Obligation to Pay.
Anything herein contained shall not in anywise limit or be construed as
limiting the Administrative Agent or the Lenders to collect the Tranche A Term
Loans or any other note, item, sum, or amount secured and to be secured hereby
only out of the revenues, monies, proceeds, benefits, and payments accruing and
to accrue unto the Issuer, under and by virtue of the Subscription Agreement,
but it is expressly understood and provided that all the Indebtedness and
amounts secured and to be secured hereby do, and shall constitute absolute and
unconditional obligations upon the Issuer to pay to the Administrative Agent
and the Lenders.

         8.3      Notices. The Purchase Notices shall be given as provided in
the Subscription Agreement. All notices and other communications provided for
herein (including, without limitation, any modifications of, or waivers or
consents under, this Agreement) shall be given or made by telex, telecopy,
courier or U.S. Mail or in writing and telexed, telecopied, mailed or delivered
to the intended recipient at the "Address for Notices" specified below its name
on the signature pages hereof or in the Loan Documents or, as to any party, at
such other address as shall be designated by such party in a notice to each
other party. Except as otherwise provided in this Agreement, all such
communications shall be deemed to have been duly given when transmitted, if
transmitted before 1:00 p.m. local time on a Business Day (as defined in the
Credit Agreement) (otherwise on the next succeeding Business Day) by telex or
telecopier and evidence or confirmation of receipt is obtained, or personally
delivered or, in the case of a mailed notice, three (3) Business Days after the
date deposited in the mails, postage prepaid, in each case given or addressed
as aforesaid.

         8.4      Amendments, Etc. Any provision of this Agreement or the
Escrow Agreement may be amended, modified or waived with the Issuer's, the
Administrative Agent's and each Equity Investor's prior written consent.

         8.5      Third-Party Beneficiaries. There shall be no third-party
beneficiaries of the Subscription Agreement other than the Administrative Agent
as provided in subsection 7.4 above.

         8.6      Agreements Cumulative. Any and all other instruments executed
or to be executed in connection with or as security for the payment of the
Indebtedness mentioned herein and secured and to be secured hereby, in law or
in equity shall be cumulative one of the other and not exclusive.


<PAGE>   8






         8.7      Governing Law. This Agreement shall be governed by, and
construed in accordance with, the laws of the State of Texas.

         8.8      Counterparts. This Agreement may be executed in any number of
counterparts, all of which taken together shall constitute one and the same
instrument and any of the parties hereto may execute this Agreement by signing
any such counterpart.

         8.9      Section Headings. The words "herein," "hereof," "hereunder"
and other words of similar import when used in this Agreement refer to this
Agreement as a whole, and not to any particular section or subsection. Any
reference herein to a Section or subsection shall be deemed to refer to the
applicable Section or subsection of this Agreement unless otherwise stated
herein. Any reference herein to an annex or exhibit shall be deemed to refer to
the applicable annex or exhibit attached hereto unless otherwise stated herein.
Captions and section headings appearing herein are included solely for
convenience of reference and are not intended to affect the interpretation of
any provision of this Agreement.

         8.10     Successors and Assigns. This Agreement shall be binding upon
and inure to the benefit of the Parties and their respective successors and
permitted assigns.

         8.11     Several Obligations. The respective obligations of the Equity
Investors hereunder are several and not joint. The failure of any Equity
Investor to perform any of its obligations hereunder shall not relieve the
other Equity Investors from any of their respective obligations hereunder.




<PAGE>   9



         IN WITNESS WHEREOF, the Parties have caused this Agreement to be
executed by their duly authorized officers as of the date first above written.



                                       ISSUER:

                                       BARGO ENERGY COMPANY

                                       By:
                                          --------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------

                                       Address for Notices:
                                                           ---------------------

                                                           ---------------------

                                                           ---------------------



                                       ADMINISTRATIVE AGENT:

                                       CHASE BANK OF TEXAS,
                                       NATIONAL ASSOCIATION, as
                                       Administrative Agent



                                       By:
                                          --------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------
                                       Address for Notices:
                                                           ---------------------

                                                           ---------------------

                                                           ---------------------



                                       ENERGY CAPITAL INVESTMENT COMPANY PLC



                                       By:
                                          --------------------------------------
                                          Gary R. Petersen
                                          Director


<PAGE>   10

                                       ENCAP ENERGY CAPITAL FUND III, L.P.
                                       By: EnCap Investments L.L.C., General
                                           Partner


                                       By:
                                          --------------------------------------
                                           D. Martin Phillips
                                           Managing Director

                                       ENCAP ENERGY CAPITAL FUND III-B, L.P.
                                       By: EnCap Investments L.L.C., General
                                           Partner



                                       By:
                                          --------------------------------------
                                           D. Martin Phillips
                                           Managing Director

                                       BOCP ENERGY PARTNERS, L.P.
                                       By: EnCap Investments L.L.C., Manager


                                       By:
                                          --------------------------------------
                                           D. Martin Phillips
                                           Managing Director

                                       EOS PARTNERS, L.P.



                                       By:
                                          --------------------------------------
                                           Brian Young
                                           General Partner







<PAGE>   11

                                       EOS PARTNERS SBIC, L.P.
                                       By: Eos SBIC General, L.P., its general
                                           partner
                                           By: Eos SBIC, Inc., its general
                                               partner



                                       By:
                                          --------------------------------------
                                           Brian Young
                                           President

                                       EOS PARTNERS SBIC II, L.P.
                                       By: Eos SBIC General II, L.P., its
                                           general partner
                                           By: Eos SBIC II, Inc., its general
                                               partner



                                       By:
                                          --------------------------------------
                                           Brian Young
                                           President


                                       SGC PARTNERS II LLC



                                       By:
                                          --------------------------------------
                                           V. Frank Pottow
                                           Managing Director

                                       BANCAMERICA CAPITAL INVESTORS SBIC I,
                                       L.P.
                                       By: BancAmerica Capital Management SBIC
                                           I, LLC, its general partner
                                           By: BancAmerica Capital Management I,
                                               L.P., its sole member
                                               By: BACM I GP, LLC, its general
                                                   partner



                                       By:
                                          --------------------------------------
                                           J. Travis Hain
                                           Managing Director









<PAGE>   12



                                       KAYNE ANDERSON ENERGY FUND, L.P.
                                       By: Kayne Anderson Capital Advisors,
                                           L.P., its General Partner
                                           By: Kayne Anderson Investment
                                               Management, Inc., its General
                                               Partner



                                       By:
                                          --------------------------------------
                                           Daniel M. Weingeist
                                           Managing Director


                                       BARGO ENERGY COMPANY



                                       By:
                                          --------------------------------------
                                           Jonathan M. Clarkson
                                           President