Exhibit (d)(5)

June 17, 2011

Brigham Exploration Company
6300 Bridgepoint Parkway
Building Two, Suite 500
Austin, Texas 78730
Attention: Eugene B. Shepherd, Jr.

Subject: Non-Solicitation Agreement

     Dear Gene:

     Statoil Texas Onshore Properties LLC, a Delaware limited liability company (together with its affiliates, “STOP”), has commenced discussions with Brigham Exploration Company, a Delaware corporation (“Target”), regarding the possible acquisition of Target by STOP (the “Proposed Transaction”). Target recognizes that STOP’S continued evaluation, pursuit and negotiation of the Proposed Transaction would require the expenditure of significant additional time, effort and resources, both internal and external, by STOP. STOP has communicated to Target that STOP will not proceed with its evaluation unless Target enters into this letter agreement. In consideration for, among other things, the willingness of STOP to devote such time, effort and resources in connection with the pursuit of the Proposed Transaction, the parties, intending to be legally bound, hereby agree as follows (this “Agreement”):

     During the period commencing on the date of this Agreement and ending on the earlier to occur of (a) 5:00 p.m., Central Daylight Time on July 15, 2011, unless extended by mutual agreement of the parties, (b) 5:00 p.m., Central Daylight Time on the business day after Target receives written notice from STOP that it is terminating negotiations of the Proposed Transaction or (c) the date of execution of a definitive agreement with respect to the Proposed Transaction or any other transaction between STOP and Target (the “Exclusivity Period”). Target shall not, and shall use its reasonable best efforts to cause its subsidiaries and its and their respective officers, directors, investment bankers, attorneys, accountants, financial advisors, agents and other representatives (collectively., the “Representatives”) not to, (i) initiate or solicit or knowingly encourage any inquiry, proposal or offer with respect to, or a transaction to effect, (x) a merger, reorganization, share exchange, consolidation, business combination, recapitalization or similar transaction involving Target or its subsidiaries, (y) any purchase or sale of 20% or more of the consolidated assets (including stock of Target’s subsidiaries) of Target and Target’s subsidiaries taken as a whole (based on fair market values), or (z) any purchase or sale of, or tender or exchange offer for Target’s securities that, if consummated, would result in any person (as used in Section 13(d) of the Securities Exchange Act of 1934) (or the stockholders of such person) beneficially owning securities representing 20% or more of the total voting power of any class of

Statoil Texas Onshore	Statoil	Telephone 713	Internet
Properties LLC	2103 City West Boulevard	713 9188200	www.stafoil. com
	Suite 800	Telefax
	Houston, Texas 77042	713 918 8290

June 17, 2011
Page 2 of 5

Target’s equity securities (any such inquiry, proposal, offer or transaction described in clauses (x), (y) or (z), an “Acquisition Proposal”), (ii) have any discussion with, or provide any confidential information to, any person relating to an Acquisition Proposal, or engage in any negotiations concerning an Acquisition Proposal, (iii) approve or recommend any Acquisition Proposal or approve any third party becoming an “interested stockholder’⁷ under Section 203 of the Delaware General Corporation Law or otherwise exempt any person or transaction from such statute, or (iv) approve or recommend or execute or enter into, any letter of intent, agreement in principle, merger agreement, acquisition agreement or other similar agreement, or agree to do any of the foregoing, related to any Acquisition Proposal or which requires Target to abandon or terminate discussions and negotiations with STOP or prohibiting any transaction with STOP that would constitute an Acquisition Proposal or (v) amend, terminate, waive, release or fail to enforce, or grant any consent under any standstill or similar agreement related to a transaction of the type included in the definition of Acquisition Proposal.

     Notwithstanding anything in this Agreement to the contrary, Target or Target’s Board of Directors may (i) engage in negotiations or discussions with, or provide any information to, any person in response to an unsolicited bona fide written Acquisition Proposal made after the date hereof that states a value or range of values and if (A) Target’s Board of Directors concludes in good faith that such Acquisition Proposal constitutes or is reasonably likely to lead to a Superior Proposal, (B) such action is necessary to comply with the fiduciary duties to Target’s shareholders under applicable law, (C) Target is not prohibited by such Acquisition Proposal or any confidentiality or agreement from complying with the provisions of this Agreement with respect to such Acquisition Proposal and (D) prior to providing any non-public information to any person in connection with such Acquisition Proposal by any such person. Target receives from such person an executed confidentiality agreement having provisions that are substantially similar to those of the Confidentiality Agreement, (ii) communicate with any person who makes such a written Acquisition Proposal solely for the purpose requesting modifications or amendments that allow compliance with clause (C) above, and (iii) comply with applicable law (including under Rule 14d-9 and Rule 14e-2 under the Securities Exchange Act of 1934) or make any other disclosure required by law or its fiduciary duties. “Superior Proposal” means an unsolicited bona fide written Acquisition Proposal for all or substantially all the equity securities or assets of Target and its subsidiaries that the Target Board of Directors determines, in good faith and after consultation with its financial advisor and outside counsel, is more favorable to the stockholders of Target than the Proposed Transaction, taking into account, among other things, the likelihood and timing of consummation and such other factors deemed relevant by the Target’s Board of Directors; provided, that any such Acquisition Proposal shall be deemed to be more favorable for purposes of this definition until STOP shall have made a written Acquisition Proposal.

     Immediately after the execution and delivery of this Agreement, Target and its subsidiaries will, and will instruct their respective Representatives to, immediately cease and terminate any existing solicitation, encouragement, discussion or negotiation with any third parties conducted heretofore by Target, its subsidiaries or any of their respective Representatives with respect to any possible Acquisition Proposal. Target agrees that it shall take all necessary

Statoil Texas Onshore	Statoil	Telephone 713	Internet
Properties LLC	2103 City West Boulevard	713 918 8200	www.stafoil. com
	Suite 800	Telefax
	Houston, Texas 77042	713 918 8290

June 17, 2011
Page 3 of 5

steps to promptly inform its Representatives involved in any prior solicitation or discussion of the types of transactions contemplated by the definition of Acquisition Proposal in this Agreement of the obligations undertaken in this Agreement. During the Exclusivity Period, Target shall notify STOP orally and in writing of the “material terms and conditions” of any offers or proposals (and any material amendments or changes thereto) provided, however, that Target shall not be required to (a) provide the identity of, and may provide the required information in such a manner as to not identify, the person who makes any such proposals or (b) provide STOP with copies of such proposals, and documents relating thereto. For purposes of the preceding sentence, “material terms and conditions” shall mean only the following (i) the value or consideration offered, (ii) the form of the consideration and if all or part is in the form of securities, the allocation as well as whether the ratio is fixed (and if not the basis for variance and any collars or walk-away rights), (iii) any conditions to acceptance of the offer or proposal and consummation of the proposed transaction, (iv) the existence of any voting agreements or proxies, (v) the material terms of any deal protection and break-up fee provisions (including the amount any such fee) and (vi) any termination rights.

     Unless and until a mutually acceptable definitive agreement between STOP and Target with respect to the Proposed Transaction has been executed and delivered, neither will be under any legal obligation to continue discussions or negotiations about, to enter into definitive agreements for, or to consummate the Proposed Transaction or any other transaction by virtue of this Agreement or any other written or oral expression with respect thereto. Neither party shall have any obligation to authorize the Proposed Transaction or any other transaction with the other party. If either party decides that it does not wish to proceed with discussions relating to the Proposed Transaction with the other party, the party so deciding agrees to promptly inform the other party of that decision; provided, however, that Target shall continue to be bound by the terms and conditions of this Agreement until its termination pursuant to the terms set forth in the second paragraph of this Agreement. This Agreement is delivered in reliance upon, and shall be held in accordance with, and treated as “Proprietary Information” (as defined in the Confidentiality Agreement) under, the provisions of that certain Confidentiality Agreement between STOP and Target dated December 29, 2010 (the “Confidentiality Agreement”); provided, however, that each party agrees that, without the prior written consent of the other party, subject to the terms hereof, it and its Representatives will not disclose to any other person (other than to its Representatives on a need to know basis) the fact that the parties have entered into this Agreement, that discussions or negotiations are taking place concerning a possible transaction or any of the terms, conditions or other facts with respect to the possible transaction (including the status hereof), it being understood, however, that notwithstanding this proviso, any party may make a disclosure otherwise prohibited by this Agreement if such disclosure is required by law and the party seeking to make such disclosures complies with the Confidentiality Agreement.

     During the Exclusivity Period, Target shall, and shall cause its Representatives, to afford to STOP and its advisors, at STOP’S sole cost and expense, reasonable access to (i) Target’s books, records, financial statements and facilities, (ii) Target’s senior executive management, and (iii) Target’s internal and external accountants and auditors for the purpose of conducting legal, accounting and commercial due diligence. In all cases, such access shall be subject to

Statoil Texas Onshore	Statoil	Telephone 713	Internet
Properties LLC	2103 City West Boulevard	713 918 8200	www.stafoil. com
	Suite 800	Telefax
	Houston, Texas 77042	713 918 8290

June 17, 2011
Page 4 of 5

reasonable restrictions so that the normal operations of Target are not unduly interrupted and coordinated by Target’s senior executive management.

     The parties to this Agreement agree that irreparable damage would occur in the event that any provision of this Agreement was not performed in accordance with the terms of this Agreement and that the parties shall be entitled to injunction and specific performance of the terms of this Agreement in addition to any other remedy at law or equity, and each party waives the need to post any bond that may be required in connection with the granting of such an injunction or other equitable relief.

     This Agreement shall be binding upon and inure solely to the benefit of the parties hereto, and nothing in this Agreement, express or implied, is intended to confer upon any other person any rights or remedies of any nature whatsoever under or by reason of this Agreement.

     This Agreement may be amended, modified or supplemented only pursuant to a written instrument signed by the parties hereto. It is understood and agreed that no failure or delay by any party in exercising any of its rights hereunder shall operate as a waiver thereof, nor shall any single or partial exercise thereof preclude any other or further exercise thereof. This Agreement, together with the Confidentiality Agreement, constitutes the entire agreement between the parties with respect to the subject matter hereof and supersedes other prior agreements and understandings, both written and oral, between the parties with respect to the subject matter hereof. This Agreement shall be governed by, enforced under and construed in accordance with the laws of the State of Delaware to the greatest extent permissible by law. This Agreement may be executed and delivered (including by facsimile transmission or .pdf) in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

[Signature Page Follows]

Statoil Texas Onshore	Statoil	Telephone 713	Internet
Properties LLC	2103 City West Boulevard	713 918 8200	www.stafoil. com
	Suite 800	Telefax
	Houston, Texas 77042	713 918 8290

June 17, 2011
Page 5 of 5

     If you are in agreement with the terms of this Agreement and desire to proceed on that basis, please sign this Agreement in the space provided below and return an executed copy to STOP, upon which this Agreement will be a binding agreement between us.

STATOIL TEXAS ONSHORE PROPERTIES LLC
By: Name:	/s/ Irene Rummelhoff Irene Rummelhoff
Title:	Vice President, Business Development

ACCEPTED AND AGREED
as of the date first written above:

BRIGHAM EXPLORATION COMPANY

By:	/s/ Eugene B. Shepherd, Jr.
Name:	Eugene B. Shepherd, Jr.
Title:	Chief Financial Officer and Executive Vice President

Statoil Texas Onshore	Statoil	Telephone 713	Internet
Properties LLC	2103 City West Boulevard	713 918 8200	www.stafoil. com
	Suite 800	Telefax
	Houston, Texas 77042	713 918 8290