Exhibit 5.1

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

May 30, 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 registration statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by the Company with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”). The Registration Statement relates to, among other things, the issuance and sale from time to time by the Company, pursuant to Rule 415 of the General Rules and Regulations promulgated under the Act, of senior debt securities, senior subordinated debt securities, subordinated debt securities and junior subordinated debt securities of the Company (collectively, the “Debt Securities”), which may be issued pursuant to an indenture between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), the form of which has been filed as an exhibit to the Registration Statement (the “Indenture”), as it may be supplemented by any supplemental indenture or officer’s certificate establishing the terms of such Debt Securities (each, a “Supplemental Indenture”).

This opinion is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of:

(i) the Registration Statement;

(ii) the form of Indenture, filed as an exhibit to the Registration Statement;

(iii) the Restated Articles of Organization of the Company, as amended to the date hereof (the “Articles of Organization”);

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(iv) the Amended and Restated Bylaws of the Company, as currently in effect (the “Bylaws”); and

(v) certain resolutions adopted on May 28, 2013 by the Board of Directors of the Company (the “Board of Directors”), relating to the registration of the Debt Securities.

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 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.

In making our examination of executed documents or documents to be executed, we have assumed that the parties thereto, other than the Company, had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents and, as to parties other than the Company, the validity and binding effect thereof on such parties. In addition, we have assumed that the terms of the Debt Securities will have been established so as not to, and that the execution and delivery by the Company of, and the performance of its obligations under, the Debt Securities, the Indenture and any Supplemental Indenture, will not (i) 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) contravene any order or decree of any governmental authority to which the Company or its property is subject, (iii) violate any law, rule or regulation to which the Company or its property is subject, or (iv) 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.

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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) we do not express any opinion with respect to the enforceability of any provision contained in the Indenture or any Supplemental 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;

(c) 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 the Indenture or any Supplemental Indenture, 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; and

(d) we do not express any opinion as to the enforceability of the provisions of the Indenture, any Supplemental Indenture or any Debt Securities providing for indemnity by any party thereto against any loss in obtaining the currency due to such party under the Indenture, such Supplemental Indenture or such Debt Securities from a court judgment in another currency.

Our opinions set forth below are limited to the Massachusetts Business Corporation Act, including, to the extent relevant, reported judicial or regulatory determinations interpreting such laws, and those laws of the State of New York that, in our experience, are normally applicable to transactions of the type contemplated by the Registration Statement 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 stated. The Debt Securities may be issued from time to time on a delayed or continuous basis, and this opinion is limited to the laws, including the rules and regulations, as in effect on the date hereof, which laws are subject to change with possible retroactive effect.

Based upon the foregoing and subject to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that, with respect to any

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series of Debt Securities (the “Offered Debt Securities”), when (i) an appropriate prospectus supplement with respect to the Offered Debt Securities has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (ii) if the Offered Debt Securities are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Debt Securities has been duly authorized, executed and delivered by the Company and the other parties thereto, (iii) the Board of Directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance and terms of the Offered Debt Securities and related matters, (iv) the Indenture, in substantially the form reviewed by us, and any Supplemental Indenture have been duly authorized, executed and delivered by each party thereto, (v) the terms of the Offered Debt Securities and of their issuance and sale have been duly established in conformity with the Indenture and any Supplemental Indenture to be entered into in connection with the issuance of the Offered Debt Securities so as not to violate the Articles of Organization or the Bylaws, and (vi) the Offered Debt Securities have been issued in a form that complies with the Indenture and have been duly executed and manually authenticated, signed or countersigned, as the case may be, in accordance with the provisions of the Indenture and any Supplemental Indenture to be entered into in connection with the issuance of the Offered Debt Securities and duly delivered to the purchasers thereof upon payment of the agreed upon consideration therefor, the Offered Debt Securities, when issued and sold in accordance with the Indenture and any Supplemental Indenture to be entered into in connection with the issuance of the Offered Debt Securities and the applicable underwriting agreement, if any, or any other duly authorized, executed and delivered valid and binding purchase or agency agreement, will be valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also hereby consent to the use of our name under the heading “Legal Matters” 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 Act or the rules and regulations of the Commission promulgated thereunder. 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