Exhibit 5.1

[Opinion of]

CRAVATH, SWAINE & MOORE LLP

[New York Office]

November 16, 2009

Mead Johnson Nutrition Company

Ladies and Gentlemen:

We have acted as counsel for the parent company of Mead Johnson Nutrition Company, a Delaware corporation (the “Company”), which is Bristol-Myers Squibb Company, a Delaware Corporation (“BMS”) in connection with the registration statement on Form S-4 (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on November 16, 2009 with respect to the offer by BMS to its common stockholders to exchange up to 170,000,000 shares of Class A common stock, par value $0.01 per share of the Company (the “Shares”), for shares of common stock, par value $0.10 per share of BMS. Of the Shares to be exchanged, 127,655,429 Shares (the “Conversion Shares” and, Shares other than the Conversion Shares, the “Outstanding Shares”) will be issued upon the conversion of Class B common stock, par value $0.01 of the Company (“Class B Shares”), prior to the consummation of the exchange offer.

In that connection, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the Registration Statement and the exhibits thereto and such documents, corporate records and other instruments as we have deemed necessary or appropriate for the purposes of this opinion, including, without limitation, (a) the Amended and Restated Certificate of Incorporation of the Company, (b) the Amended and Restated Bylaws of the Company and (c) certain resolutions adopted by the board of directors of the Company.

In rendering our opinion, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies, the authenticity of the originals of such latter documents. As to all questions of fact material to this opinion that

have not been independently established, we have relied upon certificates or comparable documents of officers and representatives of the Company and BMS.

Based on the foregoing, we are of the opinion that:

1. The Outstanding Shares are validly issued, fully paid and nonassessable.

2. The Conversion Shares, when issued upon the conversion of Class B Shares in accordance with the Company’s Amended and Restated Certificate of Incorporation, will be validly issued, fully paid and nonassessable.

We are admitted to practice in the State of New York, and we express no opinion as to any matters governed by any laws other than the laws of the State of New York, the General Corporation Law of the State of Delaware and the Federal laws of the United States of America. The reference and limitation to “Delaware General Corporation Law” includes the statutory provisions and all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Cravath, Swaine & Moore LLP

Cravath, Swaine & Moore LLP

Bristol-Myers Squibb Company

345 Park Avenue

New York, New York 10154

Mead Johnson Nutrition Company

2701 Patriot Blvd.

Glenview, Illinois 60026