

                                                                       EXHIBIT 5



          [LETTERHEAD OF VINSON & ELKINS L.L.P. APPEARS HERE]






                              May 15, 1997

Halliburton Company
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas   75201-3391

Ladies and Gentlemen:

         We  have  acted  as  counsel  for  Halliburton   Company,   a  Delaware
corporation  (the  "Company"),  for a number of years, and are familiar with the
Landmark Graphics  Corporation 1987  Non-Qualified  Stock Option Plan,  Landmark
Graphics  Corporation  1989 Flexible  Stock Option Plan,  The  Directors'  Stock
Option Plan of Landmark  Graphics  Corporation,  Landmark  Graphics  Corporation
Consultants'  Stock Option Plan,  Landmark  Graphics  Corporation  1990 Employee
Stock Option Plan and Landmark Graphics Corporation 1994 Flexible Incentive Plan
(collectively,   the  "Plans").   We  have  assisted  in  the   preparation   of
Post-Effective  Amendment No. 1 to the  Registration  Statement on Form S-8 (the
"Amendment") to be filed pursuant to the Securities Act of 1933, as amended,  on
or about May 15, 1997 with the Securities and Exchange Commission by the Company
with respect to the offering, sale and delivery of shares of Common Stock, $2.50
par value ("Common Stock") of the Company and Preferred Stock Purchase Rights of
the Company to be issued under the Plans. We note that the Plans are not subject
to the requirements of the Employee  Retirement  Income Security Act of 1974, as
amended.

         In this  connection,  we  examined  such  certificates,  documents  and
records  as we  deemed  relevant  and  necessary  as a basis  for  our  opinions
hereinafter set forth,  including,  among other things,  the Plans and copies of
relevant  resolutions  passed by the board of directors and  stockholders of the
Company.

         Based  upon the  foregoing,  we are of the  opinion  that the shares of
Common Stock to be issued upon the exercise of stock options granted pursuant to
the Plans have been validly  authorized for issuance and, (a) upon compliance by
the Company with the pertinent  provisions of any  applicable  state  securities
laws and (b)  when  the  shares  of  Common  Stock  are  issued  and paid for in
accordance  with the  terms of the  appropriate  Plan and the  underlying  stock
option, the shares of Common Stock so issued will be validly issued,  fully paid
and  nonassessable  and any  related  Preferred  Stock  Purchase  Rights will be
validly issued.




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Halliburton Company
May 15, 1997
Page 2


         This opinion is rendered as of the effective date of the Amendment.  We
hereby consent to the filing of this opinion as an exhibit to the Amendment, but
we do not admit that we are  within the  category  of persons  whose  consent is
required  under  Section  7 of the  Act  or the  rules  and  regulations  of the
Securities and Exchange Commission thereunder.

                                            Very truly yours,

                                            /s/ Vinson & Elkins L.L.P.
                                            ---------------------------
                                            VINSON & ELKINS L.L.P.





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