Exhibit 5.1

June 30, 2017

Danaher Corporation

2200 Pennsylvania Avenue NW, Suite 800W

Washington, DC 20037-1701

Re: Floating Rate Senior Notes due 2022

1.200% Senior Notes due 2027

Ladies and Gentlemen:

We have acted as U.S. counsel for DH Europe Finance S.A., a Luxembourg public limited company (the “Company”) and Danaher Corporation, a Delaware corporation (“Parent”) in connection with the issue and sale by the Company of €250,000,000 aggregate principal amount of its Floating Rate Senior Notes due 2022 (the “Floating Rate Notes”) and €600,000,000 aggregate principal amount of its 1.200% Senior Notes due 2027 (the “2027 Notes”, and together with the Floating Rate Notes, the “Notes”), pursuant to an underwriting agreement dated as of June 19, 2017 (the “Underwriting Agreement”) among the Company, Parent and the underwriters named therein. The Notes will be fully and unconditionally guaranteed as to payment of principal, premium, if any, and interest on a senior unsecured basis by Parent (the “Guarantees” and, together with the Notes, the “Securities”). The Securities will be issued pursuant to an indenture (the “Base Indenture”) dated July 8, 2015 among the Company, Parent and The Bank of New York Mellon Trust Company, N.A. as trustee (the “Trustee”), as supplemented by a Second Supplemental Indenture (the “Supplemental Indenture” and together with the Base Indenture, the “Indenture”) of even date herewith among the Company, Parent and the Trustee, and will be subject to the Paying and Calculation Agency Agreement (the “Paying and Calculation Agency Agreement”), of even date herewith among the Company, Parent, the Trustee, and The Bank of New York Mellon, London Branch, as Paying and Calculation Agent.

Parent filed with the Securities and Exchange Commission (the “Commission”) a Registration Statement on Form S-3 (File No. 333-203948) under the Securities Act of 1933, as amended (the “Securities Act”), on May 7, 2015, and Parent and the Company filed with the Commission a Post-Effective Amendment No. 1 to Registration Statement on Form S-3 (File No. 333-203948) under the Securities Act, on June 15, 2015, including the prospectus dated June 15, 2015 (the “Base Prospectus”). The Company and Parent filed with the Commission the Base Prospectus, as supplemented by the preliminary prospectus supplement dated June 19, 2017 (the “Preliminary Prospectus Supplement”) on June 19, 2017, and the final prospectus supplement dated June 19, 2017 (the “Prospectus Supplement”) on June 21, 2017.

We have examined the Indenture, the Securities, the Registration Statement, the Preliminary Prospectus Supplement and the Prospectus Supplement and we have examined and relied upon corporate or other proceedings of Parent regarding the authorization of the execution

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June 30, 2017

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and delivery of the Indenture, the Paying and Calculation Agency Agreement, the Underwriting Agreement and the issuance of the Securities, the Registration Statement, the Base Prospectus, the Preliminary Prospectus Supplement and the Prospectus Supplement. We have also examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of such other corporate records of Parent, such other agreements and instruments, certificates of public officials, directors of the Company and officers of Parent and other persons, and such other documents, instruments and certificates as we have deemed necessary as a basis for the opinions hereinafter expressed. For purposes of this opinion, we have relied without investigation on the opinion relating to matters of the laws of the Grand Duchy of Luxembourg being given on the date hereof by Luther S.A., special Luxembourg counsel for the Company.

In our examination of the documents referred to above, we have assumed the genuineness of all signatures, the legal capacity of all individual signatories, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of such original documents, and the completeness and accuracy of the corporate records of the Company and Parent provided to us by the Company and Parent.

In rendering the opinions set forth below, we have assumed (i) the due execution and delivery, pursuant to due authorization, of the Indenture by the Trustee; (ii) that the Trustee has all requisite power and authority to perform its obligations under the Indenture; (iii) the Indenture will be a valid and binding obligation of the Trustee; (iv) that the Paying and Calculation Agency Agreement will be a valid and binding obligation of the Paying and Calculation Agent and (v) the accuracy of the opinion letter, dated June 30, 2017, of Luther S.A., which is being filed as an exhibit to Parent’s Current Report on Form 8-K to be filed on the date hereof. We have also assumed that at the time of the issuance and sale of the Securities, the Board of Directors of Parent (or any committee of such Board of Directors or any person acting pursuant to authority properly delegated to such person by the Board of Directors of the Company or any committee of such Board of Directors) or the directors of the Company shall not have taken any action to rescind or otherwise reduce its prior authorization of the issuance of the Securities.

We express no opinion herein as to the laws of any jurisdiction other than the state laws of the State of New York, the General Corporation Law of the State of Delaware and the federal laws of the United States of America.

Our opinions below are qualified to the extent that they may be subject to or affected by (i) applicable bankruptcy, insolvency, reorganization, moratorium, usury, fraudulent conveyance or similar laws relating to or affecting the rights or remedies of creditors generally, (ii) duties and standards imposed on creditors and parties to contracts, including, without limitation, requirements of materiality, good faith, reasonableness and fair dealing, and (iii) general equitable principles. Furthermore, we express no opinion as to the availability of any equitable or specific remedy upon any breach of the Indenture or the Securities, or to the successful assertion

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of any equitable defenses, inasmuch as the availability of such remedies or the success of any equitable defenses may be subject to the discretion of a court. We also express no opinion herein with respect to compliance by the Company or Parent with the securities or “blue sky” laws of any state or other jurisdiction of the United States or of any foreign jurisdiction. In addition, we express no opinion and make no statement herein with respect to the antifraud laws of any jurisdiction.

On the basis of, and subject to, the foregoing, we are of the opinion that when the Securities have been duly executed by Parent and the Company and duly authenticated by the Trustee in accordance with the terms of the Indenture, and delivered to the purchasers thereof against payment of the consideration therefor in accordance with the terms of the Underwriting Agreement duly approved by Parent, the Notes will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms and the Guarantees will constitute valid and binding obligations of Parent, enforceable against Parent in accordance with their terms.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions and is rendered as of the date hereof, and we disclaim any obligation to advise you of any change in any of the foregoing sources of law or subsequent developments in law or changes in facts or circumstances that might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission as an exhibit to Parent’s Current Report on Form 8-K to be filed on the date hereof, which Form 8-K will be incorporated by reference into the Registration Statement and to the use of our name in the Preliminary Prospectus Supplement and Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.