Exhibit 5.1

[Letterhead of STvB Advocaten]

Schlumberger Limited

5599 San Felipe

17th Floor

Houston, Texas 77056

Curaçao, November 13, 2015

Ladies and Gentlemen:

We have acted as legal counsel to Schlumberger N.V. (also referred to as Schlumberger Limited), a limited liability company organized under the laws of Curaçao (“Schlumberger”), in connection with the preparation of the filing by Schlumberger of a Registration Statement on Form S-4 (the “Registration Statement”) with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of shares of common stock, par value $0.01 per share (“Common Stock”), of Schlumberger (the “Shares”) to be issued in connection with the merger of Rain Merger Sub LLC, a wholly owned subsidiary of Schlumberger Holdings Corporation (“Merger Sub”), with and into Cameron International Corporation (“Cameron”), pursuant to the Agreement and Plan of Merger dated as of August 25, 2015 among Schlumberger Holdings Corporation, an indirect wholly owned subsidiary of Schlumberger, Merger Sub, Schlumberger and Cameron (the “Merger Agreement”). Certain legal matters in connection with the Shares are being passed on for you by us. At your request, this opinion is being furnished for filing as Exhibit 5 to the Registration Statement.

This opinion is limited to matters governed by the laws of Curaçao.

We have reviewed each of the Articles of Incorporation, the Amended and Restated Bylaws of Schlumberger, each as amended to date, and the Registration Statement; have familiarized ourselves with the matters discussed in the Registration Statement; and have examined all statutes and other records, instruments and corporate documents pertaining to Schlumberger and the matters discussed in the Registration Statement that we deem necessary to examine for the purpose of this opinion. We have assumed that all signatures on all documents examined by us are genuine, that all documents submitted to us as originals are accurate and complete, that all documents submitted to us as copies are true and correct copies of the originals thereof and that all information submitted to us was accurate and complete.

In rendering this opinion, we have assumed that prior to the issuance of any of the Shares (i) the Registration Statement, as then amended, will have become effective under the Securities Act and such effectiveness shall not have been terminated or rescinded, (ii) the stockholders of Cameron will have adopted the Merger Agreement, and (iii) the other conditions to consummating the transactions contemplated by the Merger Agreement will have been satisfied and such transactions are consummated.

Based upon our examination as aforesaid, we are of the opinion that:

1. The Shares have been duly authorized by all necessary corporate action on the part of Schlumberger.

2. Upon issuance and delivery in accordance with the terms and conditions of the Merger Agreement, such Shares will be validly issued, fully paid and nonassessable.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In addition, we hereby consent to the reference of us under the caption “Legal Matters” in the proxy statement/prospectus constituting a part of the Registration Statement. In giving this consent, we do not thereby concede that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Sincerely yours,

/s/ STvB Advocaten (Curaçao) N.V.