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                                                                       EXHIBIT 5


                                [USX LETTERHEAD]


June 15, 1998


Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, D.C. 20549

Ladies and Gentlemen:

I am Assistant General Counsel-Corporate and Assistant Secretary of USX
Corporation, a Delaware corporation (hereinafter the "Corporation"), and have
served as counsel to the Corporation in connection with the preparation of the
Registration Statement on Form S-3 (hereinafter the "Registration Statement")
for the proposed issue of the Corporation's: (1) Debt Securities (the "Debt
Securities"), (2) Preferred Stock, (3) USX-Marathon Group Common Stock
("Marathon Stock"), (4) USX-U.S. Steel Group Common Stock ("Steel Stock") or
(5) Warrants to purchase Debt Securities, Preferred Stock, Marathon Stock or
Steel Stock (the "Warrants") or any combination of the foregoing at an
aggregate public offering price of $1,000,000,000. The Preferred Stock, the
Marathon Stock and the Steel Stock are collectively referred to as the
"Shares." The Warrants are to be issued pursuant to a warrant agreement between
the Corporation and a warrant agent (the "Warrant Agreement").

As Assistant General Counsel-Corporate and Assistant Secretary, I am familiar
with the Corporation's Certificate of Incorporation and its By-laws. I have
also examined, or caused those acting under my supervision to have examined,
the Registration Statement, the Indenture between the Corporation and PNC Bank,
National Association, dated as of March 15, 1993, pursuant to which the Debt
Securities will be issued (the "Indenture"), and such other records and
documents, including certificates of government officials and corporate
officers, that I have deemed necessary or desirable in rendering the opinion
set forth below. In rendering such opinion, I have presumed the genuineness of
all documents examined and the accuracy of all statements of fact contained
therein.

Based upon the foregoing, I am of the opinion that:

1.   When the Debt Securities have been duly authorized and are executed and
     authenticated in accordance with the terms of the Indenture and delivered
     to holders against receipt of payment, the Debt Securities will be legal,
     valid and binding obligations of the Corporation enforceable against it in
     accordance with the terms thereof.
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                                 LAW DEPARTMENT



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Securities and Exchange Commission
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June 15, 1998




2.   When the Shares have been duly authorized, executed by the Corporation and
     delivered against receipt of payment, the Shares will be legally issued,
     fully paid and non-assessable.

3.   When a Warrant Agreement has been prepared, executed and delivered by the
     Corporation and the Warrants have been duly authorized and duly executed in
     accordance with such Warrant Agreement and when duly paid for and delivered
     in accordance with the procedures described in the Registration Statement
     and any prospectus supplement relating to such sale, the Warrants will be
     legal, valid and binding obligations of the Corporation enforceable against
     it in accordance with and subject to the terms thereof and of such Warrant
     Agreement.

The opinions set forth above are qualified to the extent such enforceability
may be limited by any bankruptcy, insolvency, fraudulent transfer,
reorganization, moratorium and similar laws of general applicability relating
to or affecting creditors' rights and by general principles of equity.

I hereby consent to the filing of this opinion as an exhibit to the
Registration Statement.

Very truly yours,


/s/ JOHN A. HAMMERSCHMIDT
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    John A. Hammerschmidt