Exhibit 5.1

601 Lexington Avenue

New York, New York 10022

October 31, 2013

Bristol-Myers Squibb Company

345 Park Avenue

New York, New York 10154

Ladies and Gentlemen:

We have acted as special counsel to Bristol-Myers Squibb Company, a Delaware corporation (the “Company”), in connection with the registration under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and sale of (1) $500,000,000 aggregate principal amount of the Company’s 1.750% Notes due 2019 (the “2019 Notes”), (2) $500,000,000 aggregate principal amount of the Company’s 3.250% Notes due 2023 (the “2023 Notes”), and (3) $500,000,000 aggregate principal amount of the Company’s 4.500% Notes due 2044 (the “2044 Notes,” and together with the 2019 Notes and the 2023 Notes, the “Notes”), issued under an Indenture, dated as of June 1, 1993 (as heretofore supplemented, the “Indenture”), between the Company and The Bank of New York Mellon (successor to The Chase Manhattan Bank (National Association)), as trustee, and pursuant to the terms of the Underwriting Agreement, dated October 24, 2013 (the “Underwriting Agreement”), among the Company and Deutsche Bank Securities Inc., J.P. Morgan Securities LLC, Barclays Capital Inc., BNP Paribas Securities Corp., Credit Suisse Securities (USA) LLC and RBS Securities Inc., as representatives of the several underwriters named in Schedule II thereto.

The Notes were offered and sold under a registration statement on Form S-3 under the Securities Act originally filed with the Securities and Exchange Commission (the “Commission”) on July 26, 2012 (Registration No. 333-182852) (the “Registration Statement”), including a base prospectus dated July 26, 2012 (the “Base Prospectus”), and a prospectus supplement dated October 24, 2013 (together with the Base Prospectus, the “Prospectus”).

In connection with the registration of the Notes, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments as we have deemed necessary for the purposes of this opinion, including: (i) the organizational documents of the Company, including the Amended and Restated Certificate of Incorporation of the Company, as amended, (ii) minutes and records of the corporate proceedings of the Company, (iii) the Registration Statement and the exhibits thereto, and the Prospectus, (iv) the Underwriting Agreement, (v) the Indenture, and (vi) copies of all certificates and other documents delivered in connection with the sale of the Notes.

For purposes of this opinion, we have assumed the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as

copies and the authenticity of the originals of all documents submitted to us as copies. We have also assumed the legal capacity of all natural persons, the genuineness of the signatures of persons signing all documents in connection with which this opinion is rendered, the authority of such persons signing on behalf of the parties thereto other than the Company and the due authorization, execution and delivery of all documents by the parties thereto other than the Company.  We have not independently established or verified any facts relevant to the opinions expressed herein, but have relied upon statements and representations of officers and other representatives of the Company.

Based upon and subject to the qualifications, assumptions and limitations set forth herein, we are of the opinion that the Notes have been duly authorized by appropriate corporate action of the Company and constitute valid and binding obligations of the Company enforceable against the Company in accordance with their terms.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Company’s Current Report on Form 8-K and to its incorporation by reference into the Registration Statement. We also consent to the reference to our firm under the heading “Validity of the Notes” in the Prospectus constituting part of the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

We do not find it necessary for the purposes of this opinion, and accordingly we do not purport to cover herein, the application of the securities or “Blue Sky” laws of the various states to the issuance and sale of the Notes.

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. This opinion speaks only as of the date hereof and we assume no obligation to revise or supplement this opinion after the date hereof should the General Corporation Law of the State of Delaware be changed by legislative action, judicial decision or otherwise after the date hereof.

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