Exhibit 5.1

DANAHER CORPORATION

2200 PENNSYLVANIA AVENUE, N.W.

SUITE 800W

WASHINGTON, D.C. 20037-1701

TELEPHONE (202)-828-0850    FAX (202)-828-0860

May 7, 2015

Danaher Corporation

2200 Pennsylvania Avenue, NW

Suite 800W

Washington, DC 20037-1701

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

Ladies and Gentlemen:

This opinion is furnished to you in connection with a Registration Statement on Form S-3 (the “Registration Statement”), to be filed by Danaher Corporation, a Delaware corporation (the “Company”) with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of the following securities (the “Securities”) of the Company:

(i) senior debt securities (the “Senior Debt Securities”);

(ii) subordinated debt securities (the “Subordinated Debt Securities” and, together with the Senior Debt Securities, the “Debt Securities”);

(iii) common stock, $0.01 par value per share (the “Common Stock”);

(iv) preferred stock, no par value (the “Preferred Stock”);

(v) depositary shares of the Company representing a fractional interest in a share of Preferred Stock (“Depositary Shares”);

(vi) purchase contracts (“Purchase Contracts”);

(vii) units, consisting of one or more securities, including Debt Securities, Common Stock, Preferred Stock, Warrants and/or Purchase Contracts (“Units”); and

(viii) warrants to purchase Debt Securities, Common Stock, Preferred Stock or Depositary Shares, or any combination thereof (the “Warrants”);

all of which may be issued from time to time on a delayed or continuous basis pursuant to Rule 415 under the Securities Act at an indeterminate aggregate initial offering price, as set forth in the Registration Statement, the prospectus contained therein (the “Prospectus”) and any amendments or supplements thereto.

I am acting as counsel for the Company in connection with the filing of the Registration Statement. The Senior Debt Securities may be issued under the indenture (as amended or supplemented through the date of this opinion, the “Senior Indenture”) dated December 11, 2007 between the Company and The Bank of New York Mellon Trust Company, N.A., as trustee, (the “Senior Debt Trustee”). The Subordinated Debt Securities may be issued pursuant to an indenture, in the form included as Exhibit 4(e) to the Company’s Registration Statement on Form S-3 filed February 22, 2002 (SEC File No. 333-83186), to be entered into between the Company and a trustee (the “Subordinated Debt Trustee”) to be named in such indenture (the “Subordinated Indenture” and together with the Senior Indenture, the “Indentures”). The preferences, limitations and relative rights of shares of any series of Preferred Stock will be set forth in a Certificate of Designation (“Certificate of Designation”) with respect thereto. Warrants may be issued pursuant to a warrant agreement (the “Warrant Agreement”) between the Company and a bank or trust company as warrant agent. The shares of Preferred Stock represented by Depositary Shares will be deposited

pursuant to a deposit agreement (the “Deposit Agreement”) between the Company and a bank or trust company as depositary, and the preferences, limitations and relative rights of such shares of Preferred Stock will be set forth in a Certificate of Designation with respect thereto. The Purchase Contracts may be issued pursuant to a Purchase Contract Agreement (the “Purchase Contract Agreement”) between the Company and a bank or trust company as purchase contract agent. The Units may be issued pursuant to a unit agreement (the “Unit Agreement”) between the Company and a bank or trust company as unit agent.

I have examined and relied upon signed copies of the Registration Statement to be filed with the Commission, including the exhibits thereto. I have also examined and relied upon records of meetings of the Board of Directors and stockholders of the Company, the Restated Certificate of Incorporation and Amended and Restated By-Laws of the Company, each as restated and/or amended to date, and such other documents as I have deemed necessary for purposes of rendering the opinions hereinafter set forth.

In my examination of the foregoing documents, I have assumed the genuineness of all signatures, the authenticity of all documents submitted to me as originals, the conformity to original documents of all documents submitted to me as copies, the authenticity of the originals of such latter documents and the legal competence of all signatories to such documents.

I have relied as to certain matters on information obtained from public officials, officers of the Company, and other sources I believe to be reliable and I have assumed (i) that one or more prospectus supplements will have been prepared and filed with the Commission describing the Securities offered thereby, (ii) that all Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the applicable prospectus supplement, (iii) that the Subordinated Indenture will be duly authorized, executed and delivered by all parties in substantially the form filed as Exhibit 4(e) to the Company’s Registration Statement on Form S-3 filed February 22, 2002 (SEC File No. 333-83186), and that any supplemental indenture relating to a series of Debt Securities to be issued under either Indenture will be duly authorized, executed and delivered by all parties, (iv) that the Subordinated Debt Trustee shall have been qualified under the Trust Indenture Act of 1939, as amended, (v) that the Senior Debt Trustee and Subordinated Debt Trustee will be duly eligible to serve as trustee, (vi) that any Warrant Agreement, Unit Agreement, Deposit Agreement or Purchase Contract Agreement will be duly authorized, executed and delivered by all parties thereto other than the Company, (vii) that a definitive purchase, underwriting or similar agreement with respect to any Securities offered will have been duly authorized, executed and delivered by the Company and the other parties thereto, (viii) that any Securities issuable upon conversion, exchange or exercise of any Security being offered will have been duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange or exercise, (ix) with respect to shares of Common Stock or Preferred Stock offered, there will be sufficient shares of Common Stock or Preferred Stock authorized under the Company’s Restated Certificate of Incorporation and not otherwise reserved for issuance, (x) any Depositary Agreement, Purchase Contract Agreement, Unit Agreement or Warrant Agreement will be governed by New York law and (xi) that the Company will be validly existing as a corporation and in good standing under the laws of the State of Delaware at the time of the issuance of the securities.

I am expressing no opinion herein as to the application of any federal or state law or regulation to the power, authority or competence of any party to any agreement with respect to any of the Securities other than the Company. I have assumed that such agreements are, or will be, the valid and binding obligations of each party thereto other than the Company, and enforceable against each such other party in accordance with their respective terms.

I have assumed for purposes of my opinions below that no authorization, approval, consent or other action by, and no notice to or filing with, any governmental authority or regulatory body or any other third party is required for the due execution, delivery or performance by the Company or, if any such authorization, approval, consent, action, notice or filing is required, it will have been duly obtained, taken, given or made and will be in full force and effect.

I have also assumed that there will not have occurred, prior to the date of issuance of the Securities, any change in law affecting the validity or enforceability of such Securities and that at the time of the issuance and sale of the Securities, the Board of Directors of the Company (or any Committee of the Board of Directors or any member of the Board or executive officers of the Company pursuant to delegated authority from the Board of Directors) shall not have taken any action to rescind or otherwise reduce any prior authorization of the issuance of the Securities.

My 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, I express no opinion as to the availability of any equitable or specific remedy upon any breach of any of the agreements as to which I am opining herein, or any of the agreements, documents or obligations referred to therein, or to the successful assertion 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. I express no opinion herein as to the laws of any state or jurisdiction other

than the laws of the District of Columbia, the state laws of the state of New York and the General Corporation Law of the State of Delaware and the federal laws of the United States of America. I also 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, I express no opinion and make no statement herein with respect to the antifraud laws of any jurisdiction.

I also express no opinion herein as to any provision of any agreement (i) that may be deemed to or construed to waive any right of the Company, (ii) to the effect that rights and remedies are not exclusive, that every right or remedy is cumulative and may be exercised in addition to or with any other right or remedy and does not preclude recourse to one or more other rights or remedies, (iii) relating to the effect of invalidity or unenforceability of any provision of any agreement on the validity or enforceability of any other provision thereof, (iv) that is in violation of public policy, (v) relating to indemnification and contribution with respect to securities law matters, (vi) which provides that the terms of any agreement may not be waived or modified except in writing, (vii) purporting to indemnify any person against his, her or its own negligence or intentional misconduct, (viii) requiring the payment of penalties, consequential damages or liquidated damages or (ix) relating to choice of law or consent to jurisdiction.

Based upon and subject to the foregoing, I am of the opinion that:

1. With respect to the Debt Securities, when (i) specifically authorized for issuance by the Board of Directors of the Company, Committees of the Board of Directors of the Company, or records of actions of any member of the Board pursuant to delegated authority from the Board of Directors of the Company (the “Authorizing Votes”) or by executive officers of the Company pursuant to delegated authority from the Board of Directors of the Company (“Authorizing Actions”), (ii) the terms of the Debt Securities and of their issue and sale have been duly established in conformity with the applicable Indenture and assuming such terms and sale do not violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (iii) such Debt Securities have been duly executed and authenticated in accordance with the applicable Indenture and issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, and (iv) the Company has received the consideration provided for in the Authorizing Votes or Authorizing Actions, such Debt Securities will constitute valid and binding obligations of the Company.

2. With respect to shares of any series of the Preferred Stock, when (i) Authorizing Votes have specifically authorized the issuance and terms of the shares of the series, the terms of the offering thereof and related matters, including votes establishing and designating the series and fixing and determining the preferences, limitations, and relative rights thereof and the filing of a Certificate of Designation with respect to the series with the Secretary of State of the State of Delaware as required under Section 151 of the General Corporation Law of the State of Delaware, (ii) the terms of the issue and sale of the series of Preferred Stock have been duly established in conformity with the Company’s Restated Certificate of Incorporation and Amended and Restated By-Laws, each as restated and/or amended to date, and do not violate any applicable law or result in a default under or breach of any agreement or instrument binding on the Company and comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (iii) the shares of the series of Preferred Stock have been duly issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, and (iv) the Company has received the consideration provided for in the Authorizing Votes and such consideration per share is not less than the par value per share of the Preferred Stock, if any, the shares of such series of Preferred Stock will be validly issued, fully paid and nonassessable.

3. With respect to the Depositary Shares, when (i) the Authorizing Votes have specifically authorized the issuance and terms of the Depositary Shares, the terms of the offering thereof and related matters, including votes establishing and designating the series of Preferred Stock underlying the Depositary Shares and fixing and determining the preferences, limitations, and relative rights thereof and the filing of a Certificate of Designation with respect to the series of Preferred Stock underlying the Depositary Shares with the Secretary of State of the State of Delaware as required under Section 151 of the General Corporation Law of the State of Delaware, (ii) the Deposit Agreement relating to the Depositary Shares has been duly authorized, executed, and delivered and the depositary appointed by the Company, (iii) the terms of the issue and sale of the Depositary Shares have been duly established in conformity with the Company’s Restated Certificate of Incorporation and Amended and Restated By-Laws, each as restated and/or amended to date, and do not violate any applicable law or result in a default under or breach of any agreement or instrument binding on the Company and comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (iv) the Depositary Shares have been issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, (v) the shares of Preferred Stock underlying the Depositary Shares have been deposited with a bank or trust company (which meets the requirements for the depositary set forth in the Registration Statement) and (vi) the Company has received the consideration provided for in the Authorizing Votes, the Depositary Shares will be legally issued and will entitle the holders thereof to the rights specified in such Depositary Shares and the Deposit Agreement.

4. With respect to the Common Stock, when (i) specifically authorized for issuance by the Authorizing Votes, (ii) the terms of the issue and sale of the Common Stock have been duly established in conformity with the Company’s Restated Certificate of Incorporation and Amended and Restated By-Laws, each as restated and/or amended to date, and do not violate any applicable law or result in a default under or breach of any agreement or instrument binding on the Company and comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (iii) the shares of Common Stock have been issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, and (iv) the Company has received the consideration provided for in the Authorizing Votes and such consideration per share is not less than the par value per share of the Common Stock, the Common Stock will be validly issued, fully paid and nonassessable.

5. With respect to the Purchase Contracts, when (i) specifically authorized for issuance by the Authorizing Votes, (ii) the Purchase Contract Agreement has been duly authorized, executed, and delivered, (iii) the terms of the Purchase Contracts and of their issue and sale have been duly established in conformity with the Purchase Contract Agreement and do not violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and comply with any and all requirements or restrictions imposed by any court or governmental body having jurisdiction over the Company, (iv) the Purchase Contracts have been duly executed, countersigned and delivered in accordance with the Purchase Contract Agreement and issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, and (v) the Company has received the consideration provided for in the Authorizing Votes, such Purchase Contracts will constitute valid and binding obligations of the Company.

6. With respect to the Units, when (i) specifically authorized for issuance by the Authorizing Votes, (ii) the Unit Agreement has been duly authorized, executed, and delivered, (iii) the terms of the Units and of their issue and sale have been duly established in conformity with the Unit Agreement and do not violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and comply with any and all requirements or restrictions imposed by any court or governmental body having jurisdiction over the Company, (iv) the Units have been duly executed, countersigned and delivered in accordance with the Unit Agreement and issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, and (v) the Company has received the consideration provided for in the Authorizing Votes, such Units will constitute valid and binding obligations of the Company.

7. With respect to the Warrants, when (i) in the case of Warrants to purchase Common Stock, Preferred Stock or Depositary Shares, specifically authorized for issuance by the Authorizing Votes, and in the case of Warrants to purchase Debt Securities, specifically authorized for issuance by Authorizing Votes or Authorizing Actions, (ii) the Warrant Agreement relating to the Warrants has been duly authorized, executed, and delivered, (iii) the terms of the Warrants and of their issue and sale have been duly established in conformity with the Warrant Agreement relating to the Warrants and do not violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and comply with any and all requirements or restrictions imposed by any court or governmental body having jurisdiction over the Company, (iv) the Warrants have been duly executed, countersigned and delivered in accordance with the Warrant Agreement relating to the Warrants and issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplements to such Prospectus, and (v) the Company has received the consideration provided for in the Authorizing Votes or Authorizing Actions, such Warrants will constitute valid and binding obligations of the Company.

Please note that I am 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 I disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

I hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act and to the use of my name therein and in the related Prospectus and any prospectus supplement under the caption “Legal Matters.” In giving such consent, I do not hereby admit that I am in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

/s/ James F. O’Reilly

James F. O’Reilly

Vice President, Associate General Counsel and Secretary