Exhibit 5.1

OPINION OF DAVIS POLK & WARDWELL LLP

May 18, 2015

The AES Corporation

4300 Wilson Boulevard

Arlington, Virginia 22203

Ladies and Gentlemen:

The AES Corporation, a Delaware corporation (the “Company”), has filed with the Securities and Exchange Commission a Registration Statement on Form S-3 (File No. 333-186888) (the “Registration Statement”) for the purpose of registering under the Securities Act of 1933, as amended (the “Securities Act”), certain securities, including up to 59,468,788 shares (the “Shares”) of common stock, par value $0.01 per share (the “Common Stock”) of the Company. The Shares are to be sold pursuant to an underwriting agreement dated May 12, 2015 (the “Underwriting Agreement”) among the Company, Terrific Investment Corporation, a corporation incorporated under the laws of the People’s Republic of China, and Morgan Stanley & Co. LLC, as underwriter.

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinion expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all signatures on all documents that we reviewed are genuine, (iv) all natural persons executing documents had and have the legal capacity to do so, (v) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vi) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

Based on the foregoing, we advise you that, in our opinion, the Shares are validly issued, fully paid and non-assessable.

We are members of the Bar of the State of New York and the foregoing opinion is limited to the laws of the State of New York and General Corporation Law of the State of Delaware.

We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K to be filed by the Company on the date hereof and its incorporation by reference into the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the prospectus supplement dated May 12, 2015, which is a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP