Exhibit 5.1

Hogan Lovells US LLP Columbia Square 555 Thirteenth Street, NW Washington, DC 20004 T +1 202 637 5600 F +1 202 637 5910 www.hoganlovells.com

March 2, 2018

Board of Directors

Anthem, Inc.

120 Monument Circle

Indianapolis, Indiana 46204-4903

Ladies and Gentlemen:

We are acting as special counsel to Anthem, Inc., an Indiana corporation (the “Company”), in connection with the Underwriting Agreement, dated February 28, 2018 (the “Underwriting Agreement”), among the Company and Barclays Capital Inc., Credit Suisse Securities (USA) LLC, and Morgan Stanley & Co. LLC, as representatives (the “Representatives”) of the several Underwriters named in Exhibit B thereto (the “Underwriters”), and the Selling Securityholders named on Exhibit A thereto providing for the purchase by the Underwriters from the Company, upon the terms and conditions set forth in the Underwriting Agreement, of $850,000,000 aggregate principal amount of the Company’s 4.550% Notes due 2048 (the “Primary Notes,”) and the purchase by the Underwriters from the Selling Securityholders, upon the terms and conditions set forth in the Underwriting Agreement of $1,250,000,000 aggregate principal amount of the Company’s 4.101% Notes due 2028 (the “Secondary Notes” and collectively with the Primary Notes, the “Notes”) pursuant to the Company’s automatic shelf registration statement on Form S-3 (333-221824) filed with the Securities and Exchange Commission (the “SEC”) on November 30, 2017 (the “Registration Statement”). The Primary Notes were issued and sold by the Company pursuant to the terms of the Underwriting Agreement. The Secondary Notes were sold by the Selling Securityholders pursuant to the Underwriting Agreement.

This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation

S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including pdfs). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

Board of Directors

Anthem, Inc.

March 2, 2018

Page 3

For the purposes of this opinion letter, we have assumed that (i) The Bank of New York Mellon Trust Company, N.A., as trustee (the “Trustee”) under the Indenture, dated as of November 21, 2017, between the Company and the Trustee, filed as Exhibit 4.1 to the Company’s Form 8-K dated November 21, 2017, and incorporated into the Registration Statement by reference (the “Indenture”), has all requisite power and authority under all applicable laws, regulations and governing documents to execute, deliver and perform its obligations under the Indenture and has complied with all legal requirements pertaining to its status as such status relates to the Trustee’s right to enforce the Indenture against the Company, (ii) the Trustee has duly authorized, executed and delivered the Indenture, (iii) the Trustee is validly existing and in good standing in all necessary jurisdictions, (iv) the Indenture constitutes a valid and binding obligation, enforceable against the Trustee in accordance with its terms, (v) there has been no material mutual mistake of fact or misunderstanding or fraud, duress or undue influence in connection with the negotiation, execution and delivery of the Indenture, and the conduct of all parties to the Indenture has complied with any requirements of good faith, fair dealing and conscionability, and (vi) there are and have been no agreements or understandings among the parties, written or oral, and there is and has been no usage of trade or course of prior dealing among the parties that would, in either case, define, supplement or qualify the terms of the Indenture. We also have assumed the validity and constitutionality of each relevant statute, rule, regulation and agency action covered by this opinion letter.

This opinion letter is based as to matters of law solely on the applicable provisions of the laws of the State of New York (but not including any laws, statutes, ordinances, administrative decisions, rules or regulations of any political subdivision below the state level), as currently in effect. We express no opinion herein as to any other laws, statutes, ordinances, rules, or regulations (and in particular, we express no opinion as to any effect that such other laws, statutes, ordinances, rules, or regulations may have on the opinion expressed herein). Insofar as the opinion expressed herein relates to or is dependent upon matters governed by Indiana law, we have relied, without independent investigation, upon, and our opinion expressed herein is subject to all of the qualifications, assumptions and limitations expressed in, the opinion of Faegre Baker Daniels, LLP, special counsel to the Company in the State of Indiana. A copy of such opinion letter, dated as of the date hereof, is to be filed as Exhibit 5.2 to the Current Report on Form 8-K relating to the offer and sale of the Notes described below.

Based upon, subject to and limited by the foregoing, we are of the opinion that:

(a) The Primary Notes have been duly authorized on behalf of the Company and that, following (i) receipt by the Company of the consideration for the Primary Notes specified in the Underwriting Agreement and (ii) the due execution, authentication, issuance and delivery of the Primary Notes pursuant to the terms of the Indenture, the Primary Notes will constitute valid and binding obligations of the Company.

(b) The Secondary Notes have been duly authorized on behalf of the Company and constitute valid and binding obligations of the Company.

This opinion letter has been prepared for use in connection with the filing by the Company of a Current Report on Form 8-K on the date hereof, which Form 8-K will be incorporated by reference into the Registration Statement and speaks as of the date hereof. We assume no obligation to advise you of any changes in the foregoing subsequent to the delivery of this letter. We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the above-described Form 8-K and to the

Board of Directors

Anthem, Inc.

March 2, 2018

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reference to this firm under the caption “Legal Matters” in the Prospectus dated February 27, 2018 that forms part of the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of Section 11 of the Securities Act of 1933, as amended.

Very truly yours,

/s/ Hogan Lovells US LLP

HOGAN LOVELLS US LLP