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                                                                      Exhibit 5



                                   June 5, 1998


Brigham Exploration Company
6300 Bridge Point Parkway
Building Two, Suite 500
Austin, Texas 78730

Dear Sirs and Madams:

         We have acted as counsel for Brigham Exploration Company, a Delaware
corporation (the "Company"), in connection with the preparation of the Company's
Registration Statement on Form S-1 (Registration No. 333-53873), as amended (the
"Registration Statement"), filed with the Securities and Exchange Commission
under the Securities Act of 1933, as amended, relating to the proposed offering
of 3,400,000 shares (the "Shares") of the Company's common stock, par value $.01
per share (the "Common Stock"), together with 510,000 additional shares of
Common Stock (the "Additional Shares") subject to the underwriters'
over-allotment option as described in the Registration Statement.

         In connection with the foregoing, we have examined the originals or
copies, certified or otherwise authenticated to our satisfaction, of the
Registration Statement and such corporate records of the Company, certificates
of public officials and of officers of the Company, and other agreements,
instruments and documents as we have deemed necessary as a basis for the
opinions hereinafter expressed. Where facts material to the opinions hereinafter
expressed were not independently established by us, we have relied upon the
statements of officers of the Company, where we deemed such reliance appropriate
under the circumstances.

         Based upon the foregoing and in reliance thereon, and subject to the
assumptions and qualifications hereinafter specified, it is our opinion that:

         1. The Company is a corporation duly incorporated under the laws of the
State of Delaware.

         2. Upon (a) the taking of action by the duly authorized Pricing
Committee of the Board of Directors of the Company to determine the price at
which the Shares and Additional Shares are to be sold under the Underwriting
Agreement and (b) the sale of the Shares and the Additional Shares in accordance
with the terms of the Underwriting Agreement for the price so determined, the
Shares and any Additional Shares will be duly authorized by all necessary
corporate action on the part of the Company, legally issued, fully paid and
nonassessable.


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Brigham Exploration Company
June 5, 1998
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         We hereby consent to the filing of this opinion as Exhibit 5 to the
Registration Statement and to the reference to us under the caption "Legal
Matters" in the prospectus forming a part of the Registration Statement. In
giving this consent, we do not thereby admit that we are within the category of
persons whose consent is required under Section 7 of the Securities Act or the
rules or regulations of the Commission thereunder.

                                      Respectfully submitted,

                                      THOMPSON & KNIGHT,
                                      A Professional Corporation



                                      By:  /s/ Joe Dannenmaier
                                          ------------------------------
                                          Joe Dannenmaier, Attorney