Exhibit 5.1

[LETTERHEAD OF SKADDEN, ARPS, SLATE, MEAGHER & FLOM LLP]

June 6, 2013

EMC Corporation

176 South Street

Hopkinton, Massachusetts 01748

Re: Registration Statement on Form S-3 of EMC Corporation

Ladies and Gentlemen:

We have acted as special counsel to EMC Corporation, a Massachusetts corporation (the “Company”), in connection with the public offering of $2,500,000,000 aggregate principal amount of the Company’s 1.875% Notes due 2018, $2,000,000,000 aggregate principal amount of the Company’s 2.650% Notes due 2020 and $1,000,000,000 aggregate principal amount of the Company’s 3.375% Notes due 2023 (collectively, the “Securities”), issuable under the Indenture, dated as of June 6, 2013 (the “Base Indenture”) between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), as supplemented by the officer’s certificate, dated the date hereof, establishing the terms of such Securities (together with the Base Indenture, the “Indenture”). On June 3, 2013 the Company entered into an Underwriting Agreement (the “Underwriting Agreement”), with Citigroup Global Markets Inc., J.P. Morgan Securities LLC and Merrill Lynch, Pierce, Fenner & Smith Incorporated, as representatives of the several underwriters named therein (the “Underwriters”), relating to the sale by the Company to the Underwriters of the Securities.

This opinion is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Securities Act”).

In rendering the opinions set forth herein, we have examined and relied on the following:

(i) the registration statement on Form S-3 (File No. 333-188933) of the Company relating to the Securities and other securities of the Company filed with the Securities and Exchange Commission (the

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“Commission”) on May 30, 2013 under the Securities Act allowing for delayed offerings pursuant to Rule 415 of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”), including information deemed to be a part of the registration statement pursuant to Rule 430B of the Rules and Regulations (such registration statement, being hereinafter referred to as the “Registration Statement”);

(ii) the global certificates evidencing the Securities (the “Note Certificates”) in the form delivered by the Company to the Trustee for authentication and delivery;

(iii) an executed copy of the Indenture;

(iv) an executed copy of the Underwriting Agreement;

(v) an executed copy of a certificate of Paul T. Dacier, Executive Vice President and General Counsel of the Company, dated the date hereof (the “Secretary’s Certificate”);

(vi) a copy of the Company’s Restated Articles of Organization, certified by the Secretary of the Commonwealth of the Commonwealth of Massachusetts as of May 28, 2013, and certified pursuant to the Secretary’s Certificate;

(vii) a copy of the Company’s Amended and Restated Bylaws, as amended and in effect as of the date hereof, certified pursuant to the Secretary’s Certificate; and

(viii) a copy of certain resolutions of the Board of Directors of the Company, adopted on May 28, 2013, and certain resolutions of the Finance Committee thereof, adopted on June 3, 2013, certified pursuant to the Secretary’s Certificate.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions set forth below.

In our examination, we have assumed the genuineness of all signatures, including endorsements, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original

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documents of all documents submitted to us as facsimile, electronic, certified or photostatic copies, and the authenticity of the originals of such copies. As to any facts relevant to the opinions stated herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

Our opinions set forth herein are limited to the Massachusetts Business Corporation Act (the “MBCA”), including, to the extent relevant, reported judicial or regulatory determinations interpreting such laws, and the laws of the State of New York that, in our experience, are applicable to transactions of the type covered by the Underwriting Agreement, the Indenture and the Securities and, to the extent that judicial or regulatory orders or decrees or consents, approvals, licenses, authorizations, validations, filings, recordings or registrations with governmental authorities are relevant, to those required under such laws (all of the foregoing being referred to as “Opined on Law”). We do not express any opinion with respect to the law of any jurisdiction other than Opined on Law or as to the effect of any such non-Opined on Law on the opinions herein which laws are subject to change with possible retroactive effect. This opinion is limited to the laws as in effect on the date hereof, which laws are subject to change with possible retroactive effect.

The Indenture and the Note Certificates are referred to herein collectively as the “Transaction Agreements.”

Based upon the foregoing and subject to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that the Securities have been duly authorized by all requisite corporate action on the part of the Company and duly executed by the Company under the MBCA, and when duly authenticated by the Trustee and issued and delivered by the Company against payment therefor in accordance with the terms of the Underwriting Agreement and the Indenture, the Securities will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms under the laws of the State of New York.

The opinions stated herein are subject to the following qualifications:

(a) the opinions stated herein are limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer, preference and other similar laws affecting creditors’ rights generally, and by general principles of equity (regardless of whether enforcement is sought in equity or at law);

(b) except to the extent expressly stated in the opinions contained herein, we do not express any opinion with respect to the effect on the opinions stated herein of (i) the compliance or non-compliance of any party to any of the Transaction Agreements with any laws, rules or regulations applicable to such party or (ii) the legal status or legal capacity of any such party to any of the Transaction Agreements;

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(c) except to the extent expressly stated in the opinions contained herein, we have assumed that each of the Transaction Agreements constitutes the valid and binding obligation of each party to such Transaction Agreement, enforceable against such party in accordance with its terms;

(d) we do not express any opinion with respect to the enforceability of any provision contained in the Indenture relating to any indemnification, contribution, exculpation, release or waiver that may be contrary to public policy or violative of federal or state securities laws, rules or regulations; and

(e) to the extent that any opinion relates to the enforceability of the choice of New York law and choice of New York forum provisions contained in any Transaction Agreement, the opinions stated herein are subject to the qualification that such enforceability may be subject to, in each case, (i) the exceptions and limitations in New York General Obligations Law sections 5-1401 and 5-1402, and (ii) principles of comity or constitutionality.

In addition, in rendering the foregoing opinions, we have assumed that neither the execution and delivery by the Company of the Transaction Agreements nor the consummation by the Company of the transactions contemplated thereby, including the issuance and sale of the Securities: (i) constitutes or will constitute a violation of, or a default under, any lease, indenture, instrument or other agreement to which the Company or its property is subject, (ii) contravenes or will contravene any order or decree of any governmental authority to which the Company or any of its property is subject, (iii) violates or will violate any law, rule or regulation to which the Company or its property is subject or (iv) requires or will require the consent, approval, licensing or authorization of, or any filing, recording or registration with, any governmental authority under any law, rule or regulation of any jurisdiction.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K, being filed on the date hereof, and incorporated by reference into the Registration Statement. We also hereby consent to the use of our name under the heading “Legal Matters” in the prospectus supplement dated June 3, 2013 and in the prospectus which forms a part of the Registration Statement. In giving this consent, 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. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

Very truly yours,

/s/ Skadden, Arps, Slate, Meagher & Flom LLP