<PAGE>

                                                                    Exhibit 10.5
                      FIFTH AMENDMENT TO CREDIT AGREEMENT


     THIS FIFTH AMENDMENT TO CREDIT AGREEMENT (this "Amendment") is among: EEX
CORPORATION (formerly known as ENSERCH EXPLORATION, INC.), a corporation formed
under the laws of the State of Texas (the "Company"); each of the Lenders (as
defined in the Credit Agreement as hereafter defined) that is a signatory
hereto; THE CHASE MANHATTAN BANK, a  New York banking corporation (in its
individual capacity, "Chase"), as administrative agent for the Lenders (in such
capacity, together with its successors in such capacity, the "Administrative
Agent"); as auction agent for the Lenders (in such capacity, together with its
successors in such capacity, the "Auction Agent"); and as book runner for the
Lenders (in such capacity, together with its successors in such capacity, the
"Book Runner"); The First National Bank of Chicago, a national banking
association (in its individual capacity, "First Chicago") and as syndication
agent for the Lenders (in such capacity, together with its successors in such
capacity, the "Syndication Agent"); Citibank, N.A.  a national banking
association (in its individual capacity, "Citibank") and as a documentation
agent for the Lenders (in such capacity, together with its successors in such
capacity, a "Documentation Agent"); Canadian Imperial Bank of Commerce as a
documentation agent for the Lenders (in such capacity, together with its
successors in such capacity, a "Documentation Agent") and The Bank of New York,
The Bank of Nova Scotia, Bankers Trust Company, NationsBank of Texas, N.A. and
Royal Bank of Canada as co-agents (in such capacity, together with their
successors in such capacity, the Co-Agents").


                                 R E C I T A L S
                                 ---------------

     A.  The Company, the Agents, and the Lenders  have entered into that
certain Credit Agreement dated as of May 1, 1995 as amended by First Amendment
to Credit Agreement dated as of September 16, 1996, by Second Amendment to
Credit Agreement dated as of June 27, 1997, by Third Amendment to Credit
Agreement dated as of September 25, 1997 and by Fourth Amendment to Credit
Agreement dated as of December 15, 1997 (collectively, the "Credit Agreement"),
pursuant to which the Lenders have agreed to make certain loans and extensions
of credit to the Company upon the terms and conditions as provided therein; and

     B.  The Company, the Agents, and the Lenders now desire to make certain
amendments to the Credit Agreement.

     NOW, THEREFORE, in consideration of the premises and other good and
valuable consideration and the mutual benefits, covenants and agreements herein
expressed, the parties hereto now agree as follows:

     1.  All capitalized terms used in this Amendment and not otherwise defined
herein shall have the meanings ascribed to such terms in the Credit Agreement.

     2.  The definitions of "Agents", "Agreement", and "Applicable Margin" in
Section 1.02 of the Credit Agreement are hereby amended to read as follows:

          "Agents" shall  mean the Administrative Agent, the Syndication Agent,
     the Documentation Agents, the Book Runner, the Auction Agent and the Co-
     Agents.
<PAGE>

          "Agreement" shall mean this Credit Agreement as amended by First
     Amendment, Second Amendment, Third Amendment, Fourth Amendment and Fifth
     Amendment as the same may from time to time be amended or supplemented.

          "Applicable Margin" shall mean the following rates per annum as are
     applicable based upon the Debt to Capital Ratio calculated as of the last
     day of a fiscal quarter of the Company to be effective for any Committed
     Loan outstanding or for the facility fee during the period from the
     Financial Statement Delivery Date following such fiscal quarter to but not
     including the next succeeding Financial Statement Delivery Date:


                                       DEBT TO CAPITAL RATIO
                                       ---------------------

                                       25%*        35%*      45%*
                                       but         but      but
                             25%**     35%**       45%**    55%**      55%**
                             ----      ----        ----     -----      -----
------------------------------------------------------------------------------

Facility Fee                 .200%     .250%       .300%    .400%       .450%
------------------------------------------------------------------------------

Eurodollar Loans             .550%     .750%       .950%   1.100%      1.300%
------------------------------------------------------------------------------

Base Rate Loans                 0%        0%          0%       0%          0%
------------------------------------------------------------------------------

*  greater than or equal to
** less than

     4.   Section 1.02 of the Credit Agreement is hereby supplemented, where
alphabetically appropriate, with the addition of the following definition:

          "Fifth Amendment" shall mean that certain Fifth Amendment to Credit
     Agreement dated as of March 31, 1999, among the Company, the Lenders and
     the  Agents."

     5.  The second sentence of Section 11.01 of the Credit Agreement is hereby
amended to read as follows:

          "The Syndication Agent, the Documentation Agents, the Book Runner and
     Co-Agents, in such capacities, shall have no duties or responsibilities and
     shall incur no liabilities under the Loan Documents."

     6.  This Amendment shall become binding on the Lenders when, and only when,
the Administrative Agent shall have received each of the following in form and
substance satisfactory to the Administrative Agent or its counsel:

          (a) counterparts of this Amendment and the attached Ratification
     executed by the Company, the Guarantors and the Majority Lenders;

          (b) a certificate of the Secretary or an Assistant Secretary of the
     Company setting forth resolutions of its board of directors with respect to
     the authorization of the Company to execute, deliver and perform this
     Amendment; and

                                       2
<PAGE>

          (c) such other documents as it or its counsel may reasonably request.

     7.  The parties hereto hereby acknowledge and agree that, except as
specifically supplemented and amended, changed or modified hereby, the Credit
Agreement shall remain in full force and effect in accordance with its terms.

     8.  The Company hereby reaffirms that as of the date of this Amendment, the
representations and warranties contained in Article VII of the Credit Agreement
are true and correct on the date hereof as though made on and as of the date of
this Amendment, except as such representations and warranties are expressly
limited to an earlier date.

     9.  THIS AMENDMENT (INCLUDING, BUT NOT LIMITED TO, THE VALIDITY AND
ENFORCEABILITY HEREOF) SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH,
THE LAWS OF THE STATE OF TEXAS, OTHER THAN THE CONFLICT OF LAWS RULES THEREOF.

     10.  This Amendment may be executed in two or more counterparts, and it
shall not be necessary that the signatures of all parties hereto be contained on
any one counterpart hereof; each counterpart shall be deemed an original, but
all of which together shall constitute one and the same instrument.    Delivery
of an executed signature page of this Amendment by facsimile transmission shall
be effective as delivery of a manually executed counterpart hereof.



                                 [SIGNATURES BEGIN NEXT PAGE]

                                       3
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed as of March 31, 1999.


COMPANY:                            EEX CORPORATION (formerly known as
                                    ENSERCH EXPLORATION, INC.)

                                    By:  /s/ J. T. Leary
                                       --------------------------------
                                    Name:  J. T. Leary
                                    Title: Vice President, Finance, and
                                           Treasurer


LENDER AND ADMINISTRATIVE AGENT,    THE CHASE MANHATTAN BANK
BOOK RUNNER AND
AUCTION AGENT:
                                    By:  /s/ Peter M. Ling
                                       --------------------------------
                                    Name:  Peter M. Ling
                                    Title: Vice President


LENDER AND SYNDICATION              THE FIRST NATIONAL BANK OF
AGENT                               CHICAGO

                                    By:  /s/ Ronald L. Dierker
                                       --------------------------------
                                    Name:  Ronald L. Dierker
                                    Title: Vice President


LENDER AND DOCUMENTATION            CITIBANK, N.A.
AGENT:

                                    By:  /s/ J. Christopher Lyons
                                       --------------------------------
                                    Name:  J. Christopher Lyons
                                    Title: Attorney-in-fact


LENDER AND DOCUMENTATION            CANADIAN IMPERIAL BANK OF
AGENT:                              COMMERCE


                                    By:  /s/ Michael A. G. Corkum
                                       --------------------------------
                                    Name:  Michael A. G. Corkum
                                    Title: Assistant General Manager

                                       4
<PAGE>

LENDER:                             THE BANK OF NEW YORK

                                    By:  /s/ Raymond J. Palmer
                                       --------------------------------
                                    Name:  Raymond J. Palmer
                                    Title: Vice President


LENDER:                             THE BANK OF NOVA SCOTIA

                                    By:  /s/ F. C. H. Ashby
                                       --------------------------------
                                    Name:  F. C. H. Ashby
                                    Title: Senior Manager Loan Operations


LENDER:                             BANKERS TRUST COMPANY

                                    By:  /s/ Marcus M. Tarkington
                                       --------------------------------
                                    Name:  Marcus M. Tarkington
                                    Title: Principal


LENDER:                             NATIONSBANK OF TEXAS, N.A.

                                    By:  /s/ Paul A. Squires
                                       --------------------------------
                                    Name:  Paul A. Squires
                                    Title: Senior Vice President


LENDER:                             ROYAL BANK OF CANADA

                                    By:  /s/ Gil J. Benard
                                       --------------------------------
                                    Name:  Gil J. Benard
                                    Title: Senior Manager


LENDER:                             CREDIT AGRICOLE INDOSUEZ
                                    (Formerly Caisse Nationale De Credit
                                    Agricole)

                                    By:  /s/ Brian D. Knezeak
                                       --------------------------------
                                    Name:  Brian D. Knezeak
                                    Title: First Vice President

                                    By:  /s/ Michael R. Quiray
                                       --------------------------------
                                    Name:  Michael R. Quiray
                                    Title: Vice President
                                           Senior Relationship Manager

                                       5
<PAGE>

LENDER:                             THE FUJI BANK, LTD.

                                    By:  /s/ Raymond Ventura
                                       --------------------------------
                                    Name:  Raymond Ventura
                                    Title: Vice President & Manager


LENDER:                             THE INDUSTRIAL BANK OF JAPAN TRUST COMPANY

                                    By:  /s/ Mike Oakes
                                       --------------------------------
                                    Name:  Mike Oakes
                                    Title: Senior Vice President
                                    THE INDUSTRIAL BANK OF JAPAN,
                                    LIMITED, HOUSTON OFFICE
                                    (Authorized Representative)


LENDER:                             THE LONG-TERM CREDIT BANK OF JAPAN, LTD.

                                    By:  /s/ Sadao Muraoka
                                       --------------------------------
                                    Name:  Sadao Muraoka
                                    Title: Head of Southwest Region


LENDER:                             MELLON BANK, N.A.

                                    By:  /s/ Roger E. Howard
                                       --------------------------------
                                    Name:  Roger E. Howard
                                    Title: Vice President


LENDER:                             THE SANWA BANK, LIMITED

                                    By:  /s/ Clyde Redford
                                       --------------------------------
                                    Name:  Clyde Redford
                                    Title: Vice President


LENDER:                             TORONTO DOMINION (TEXAS), INC.

                                    By:  /s/ Carol Brandt
                                       --------------------------------
                                    Name:  Carol Brandt
                                    Title: Vice President


LENDER:                             UBS AG, STAMFORD BRANCH
                                    as successor to Union Bank of Switzerland,

                                       6
<PAGE>

                                    Houston Agency

                                    By:  /s/ Paul R. Morrison
                                       --------------------------------
                                    Name:  Paul R. Morrison
                                    Title: Executive Director

                                    By:  /s/ Andrew N. Taylor
                                       --------------------------------
                                    Name:  Andrew N. Taylor
                                    Title: Associate Director


LENDER:                             THE BANK OF TOKYO-MITSUBISHI, LTD.

                                    By:  /s/ Ichiro Otani
                                       --------------------------------
                                    Name:  Ichiro Otani
                                    Title: Deputy General Manager


LENDER:                             DRESDNER BANK AG NEW YORK
                                    AND GRAND CAYMAN BRANCHES

                                    By:  /s/ Michael E. Higgins
                                       --------------------------------
                                    Name:  Michael E. Higgins
                                    Title: Vice President

                                    By:  /s/ Wendy Astell
                                       --------------------------------
                                    Name:  Wendy Astell
                                    Title: Assistant Treasurer


LENDER:                             CREDIT LYONNAIS NEW YORK BRANCH

                                    By:  /s/ Philipe Soustra
                                       --------------------------------
                                    Name:  Philipe Soustra
                                    Title: Senior Vice President

                                       7
<PAGE>

                                  RATIFICATION
                                  ------------

     Each of the undersigned (a "Guarantor") hereby agrees that its liabilities
under its respective Guaranty Agreement guaranteeing the indebtedness,
obligations and liabilities under that certain Credit Agreement dated May 1,
1995, as amended, shall remain enforceable against such Guarantor in accordance
with the terms of its Guaranty Agreement and shall not be reduced, altered,
limited, lessened or in any way affected by the execution and delivery of this
Fifth Amendment to Credit Agreement.  Each Guarantor hereby confirms and
ratifies its liabilities under its Guaranty in all respects.

                                    EEX CORPORATION (formerly known as
                                    ENSERCH EXPLORATION, INC.)

                                    By:  /s/ J. T. Leary
                                       --------------------------------
                                    Name:  J. T. Leary
                                    Title: Vice President, Finance, and
                                           Treasurer


                                    EEX OPERATING LLC
                                    By:  EEX Corporation, as sole manager

                                    By:  /s/ J. T. Leary
                                       --------------------------------
                                    Name:  J. T. Leary
                                    Title: Vice President, Finance, and
                                           Treasurer


                                    EEX OPERATING LP
                                    By:  EEX Corporation, as general partner

                                    By:  /s/ J. T. Leary
                                       --------------------------------
                                    Name:  J. T. Leary
                                    Title: Vice President, Finance, and
                                           Treasurer

                                       8