<PAGE>   1
                                                                    EXHIBIT 10.6

                     FIFTH AMENDMENT TO FINANCING AGREEMENT

         Fifth Amendment to Financing Agreement dated as of March 31, 2000 (the
"Amendment"), by and between Energy Partners, Ltd., a Delaware corporation (the
"Borrower"), and Energy Income Fund, L.P., a Delaware limited partnership
("EIF"), to that certain Financing Agreement dated as of April 15, 1998, as
amended by the First Amendment to Financing Agreement dated as of June 19, 1998,
the Second Amendment to Financing Agreement dated as of August 31, 1998, the
Third Amendment to Financing Agreement dated as of February 10, 1999, the Fourth
Amendment to Financing Agreement dated as of November 17, 1999 (as amended, the
"Financing Agreement").

                                    RECITALS

         WHEREAS, EIF has funded Loans totaling Twenty-Five Million Dollars
($25,000,000) under the Financing Agreement; and

         WHEREAS, there is currently unpaid and owing under the Loans the sum of
Ten Million Dollars ($10,000,000).

         NOW, THEREFORE, in consideration of the foregoing, and other good and
valuable consideration, the receipt and sufficiency of which are expressly
acknowledged, the parties hereby agree as follows:

         1. Capitalized terms used herein without definition shall have the
meanings specified in the Financing Agreement.

         2. In Section 2.3(a), the following is added as a third sentence:

                  "If principal and accrued interest outstanding under the Loans
         are not repaid in full on or prior to January 1, 2001, the Base
         Interest shall become fifteen percent (15%) per annum from and after
         such date."

         3. Section 2.5 of the Financing Agreement is deleted in its entirety
and replaced with the following:

                  "2.5. Repayment of Principal. To the extent not prepaid
         pursuant to Section 2.6, the entire principal amount of Loans and
         accrued and unpaid interest shall be due and payable on July 1, 2001.

         4. THIS AMENDMENT IS TO BE CONSTRUED UNDER THE LAWS OF THE COMMONWEALTH
OF MASSACHUSETTS.


<PAGE>   2


         5. Except as expressly amended hereby, the Financing Agreement remains
in full force and effect. Any references to the Financing Agreement in the Loan
Documents shall refer to the Financing Agreement as amended hereby.

         IN WITNESS WHEREOF, the parties have executed this Amendment as of the
date first written above.


                                       ENERGY PARTNERS, LTD.



                                       By: /s/ RICHARD A. BACHMANN
                                          --------------------------------------
                                           Richard A. Bachmann
                                           President and Chief Executive Officer



                                       ENERGY INCOME FUND, L. P.

                                       By: EIF General Partner, L.L.C.,
                                           its General Partner


                                           By: /s/ STEVEN P. MCDONALD
                                               --------------------------------
                                               Steven P. McDonald
                                               Vice-President