Exhibit 5.1

March 1, 2019 Danaher Corporation 2200 Pennsylvania Ave. N.W., Suite 800W Washington, D.C. 20037-1701 +1 212 230 8800 (t) +1 212 230 8888 (f) wilmerhale.com

Re:    Registration on Form S-3

Ladies and Gentlemen:

We have acted as counsel for Danaher Corporation, a Delaware corporation (the “Company”), in connection with the entry by the Company into the Underwriting Agreement, dated February 26, 2019 (the “Underwriting Agreement”), with Barclays Capital Inc. and Goldman Sachs & Co. LLC as representatives of the several underwriters named in Schedule A thereto (collectively, the “Underwriters”), in connection with the purchase by the Underwriters of 11,000,000 shares (the “Firm Shares”) of the Company’s common stock, par value $0.01 per share (the “Common Stock”), and the grant by the Company to the Underwriters of the option to purchase up to an additional 1,100,000 shares of Common Stock (together with the Firm Shares, the “Offering Shares”).

As such counsel, we have assisted in the preparation and filing with the Securities and Exchange Commission (the “Commission”) of (i) the Registration Statement on Form S-3 (File No. 333-224149) under the Securities Act of 1933, as amended (the “Securities Act”), on April 5, 2018 (the “Registration Statement”), including the prospectus, dated April 5, 2018 (the “Base Prospectus”), as supplemented by the preliminary prospectus supplement, dated February 26, 2019 (the “Preliminary Prospectus Supplement”), (ii) the prospectus supplement, dated February 26, 2019 (the “Prospectus Supplement”), and (iii) the final term sheet relating to the offering of the Offering Shares, dated February 26, 2019 (the “Term Sheet”).

We have examined and relied upon (i) corporate or other proceedings of the Company regarding the authorization, execution and delivery of the Underwriting Agreement and the issuance of the Shares, (ii) the Registration Statement, (iii) the Base Prospectus, (iv) the Preliminary Prospectus Supplement, (v) the Prospectus Supplement, (vi) the Term Sheet, (vii) the Underwriting Agreement, (viii) the Company’s Amended and Restated Certificate of Incorporation, as amended and (viii) the Company’s Bylaws, as amended. We have also examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of such other corporate records of the Company, such other agreements and instruments, certificates of public officials, officers of the Company and other persons, and such other documents, instruments and certificates as we have deemed necessary as a basis for the opinions hereinafter expressed.

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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 provided to us by the Company.

We express no opinion herein as to the laws of any state or jurisdiction other than the General Corporation Law of the State of Delaware. We express no opinion herein with respect to compliance by the Company with 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 the Offering Shares have been duly authorized for issuance and, when the Offering Shares are issued and delivered to and paid for by the Underwriters in accordance with the terms and conditions of the Underwriting Agreement, will be validly issued, fully paid and non-assessable.

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 the Company’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 therein and in the related Base Prospectus, 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.

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Very truly yours,
WILMER CUTLER PICKERING HALE AND DORR LLP
By:	/s/ Erika L. Robinson
	Erika L. Robinson, a Partner