EXHIBIT 5

                                                                    July 3, 1996

American Exploration Company
1331 Lamar
Suite 900
Houston, Texas 77010-3088

Dear Gentlemen:

            Reference is made to the proposed registration by American
Exploration Company, a Delaware corporation (the "Company"), of 150,000 shares
of common stock, par value $.05 per share ("Common Stock"), as contemplated by
the Company's Registration Statement on Form S-3, filed with the Securities and
Exchange Commission under the Securities Act of 1933, as amended, (the
"Registration Statement").

            As set forth in the Registration Statement, certain legal matters
are being passed on for you by us. At your request, this opinion of counsel is
being furnished to you for filing as Exhibit 5 to the Registration Statement. In
such capacity, we have examined the Articles of Incorporation and Bylaws of the
Company, and have examined all statutes and other records, instruments and
documents pertaining to the Company that we have deemed necessary to examine for
the purposes of this opinion.

            Based upon our examination as aforesaid, we are of the opinion that:

            1. The Company is a corporation duly incorporated, validly existing
      and in good standing under the laws of the State of Delaware.

            2. The shares of Common Stock registered pursuant to the
      Registration Statement constitute duly authorized and validly issued,
      fully paid and nonassessable shares of Common Stock and no personal
      liability will attach to ownership thereof under the laws of the State of
      Delaware.

            The opinions expressed in this letter are solely for use by the
company in filing the Registration Statement and these opinions may not be
relied on by any other person without our prior written approval.

                                Very truly yours,

                                Baker & Botts, L.L.P.