Exhibit 5.1

November 17, 2015

Moody’s Corporation

7 World Trade Center at 250 Greenwich Street

New York, New York, 10007

Re: Moody’s Corporation

$300,000,000 of 5.250% Senior Notes due 2044

Ladies and Gentlemen:

We have examined the Registration Statement on Form S-3, file no. 190259 (the “Registration Statement”) of Moody’s Corporation (the “Company”), filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933 (as amended, the “Securities Act”), the prospectus included therein, the prospectus supplement, dated November 12, 2015, filed with the Commission on November 12, 2015 pursuant to Rule 424(b) of the Securities Act (the “Prospectus Supplement”), in connection with the offering and sale by the Company of $300,000,000 aggregate principal amount of the Company’s 5.250% Senior Notes due July 15, 2044 (the “Notes”).

The Notes have been issued pursuant to the Indenture dated as of August 19, 2010 (as so amended prior to the date hereof, the “Base Indenture”), between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), as supplemented by the Fourth Supplemental Indenture, dated July 16, 2014 (the “Supplemental Indenture” and together with the Base Indenture, the “Indenture”) between the Company and the Trustee.

In arriving at the opinions expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of the Base Indenture, the Supplemental Indenture and the Notes and such other documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render these opinions. In our examination, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. As to any facts material to these opinions, we have relied to the extent we deemed appropriate and without independent investigation upon statements and representations of officers and other representatives of the Company and others.

Based upon the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Notes are legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

Moody’s Corporation

November 17, 2015

Page 2

The opinion expressed above is subject to the following additional exceptions, qualifications, limitations and assumptions:

A. We render no opinion herein as to matters involving the laws of any jurisdiction other than the State of New York. This opinion is limited to the effect of the current state of the laws of the State of New York and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

B. The opinion above is subject to (i) the effect of any bankruptcy, insolvency, reorganization, moratorium, arrangement or similar laws affecting the rights and remedies of creditors’ generally, including the effect of statutory or other laws regarding fraudulent transfers or preferential transfers, and (ii) general principles of equity, including concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance, injunctive relief or other equitable remedies regardless of whether enforceability is considered in a proceeding in equity or at law.

C. We express no opinion regarding the effectiveness of (i) any waiver of stay, extension or usury laws or of unknown future rights, (ii) provisions relating to indemnification, exculpation or contribution, to the extent such provisions may be held unenforceable as contrary to public policy or federal or state securities laws; (iii) any waiver of the right to jury trial; or (iv) any provision to the effect that every right or remedy is cumulative and may be exercised in addition to any other right or remedy or that the election of some particular remedy does not preclude recourse to one or more others.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Validity of Securities” in the Registration Statement and “Validity of Notes” in the Prospectus Supplement. In giving these consents, we do not thereby admit 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 Commission promulgated thereunder.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP