July 6, 1998




ENSCO International Incorporated
2700 Fountain Place
1445 Ross Avenue
Dallas, Texas  75202-2792

Gentlemen:

      ENSCO International Incorporated,  a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission") a
registration  statement  (the  "Registration  Statement")  on Form S-8 under the
Securities  Act of 1933,  as amended (the  "Act").  The  Registration  Statement
covers  11,300,000  shares of common stock,  par value $.10 per share (including
the preferred share purchase rights attaching thereto,  the "Common Stock"),  of
the Company,  and such additional  shares of Common Stock as may become issuable
pursuant to the anti-dilution  provisions of the Plan (such shares  collectively
referred to as the  "Securities").  Such Securities are to be issued pursuant to
the Company's 1998 Incentive Plan (the "Plan").

      We have acted as counsel to the Company in connection with the preparation
and filing of the  Registration  Statement.  In  rendering  this opinion we have
examined such corporate  records,  documents and  instruments of the Company and
such certificates of public officials,  have received such  representations from
officers of the  Company,  and have  reviewed  such  questions  of law as in our
judgment  are  necessary,  relevant  or  appropriate  to enable us to render the
opinion expressed below. In such examination, we have assumed the genuineness of
all  signatures,  the  authenticity  of all  corporate  records,  documents  and
instruments  submitted to us as originals,  the conformity to original documents
of all documents  submitted to us as conformed,  certified or photostatic copies
thereof, and the authenticity of the originals of such photostatic, certified or
conformed copies.

      Based upon such examination and review and upon representations made to us
by  officers  of the  Company,  we are of the  opinion  that upon  issuance  and
delivery of the  Securities in accordance  with the terms and  conditions of the
Plan,  and  upon  receipt  by the  Company  of the  full  consideration  for the
Securities as determined  pursuant to the Plan, the  Securities  will be legally
issued, fully paid and nonassessable shares of Common Stock.

      This firm  consents  to the  filing of this  opinion  as an exhibit to the
Registration  Statement.  In giving such  consent,  we do not admit that we come
within the category of persons whose consent is required by Section 7 of the Act
or the rules and regulations of the Commission thereunder.

                                    Respectfully submitted,

                                    /s/ BAKER & MCKENZIE