Exhibit (a)(5)(D)

KINDRED HEALTHCARE RESPONDS TO GENTIVA

Gentiva Is Preventing Its Shareholders from Receiving an Immediate and Certain 70% Cash Premium

Gentiva Has Not Demonstrated How It Would Create Value Greater Than Kindred Is Offering

Kindred Urges Gentiva Shareholders to Tender their Shares in Support of its Value Enhancing Offer

LOUISVILLE, Ky. (July 1, 2014) – Kindred Healthcare, Inc. (“Kindred” or the “Company”) (NYSE:KND) today responded to the decision by the board of directors of Gentiva Health Services, Inc. (“Gentiva”) (NASDAQ:GTIV) recommending against Kindred’s offer to acquire all of Gentiva’s outstanding common stock for $14.50 per share in cash.

Paul J. Diaz, Chief Executive Officer of Kindred, said, “After reviewing Gentiva’s recommendation, it remains clear that Kindred’s offer would create immediate, certain and superior value for Gentiva shareholders. We call on the Gentiva board and management team to sit down and negotiate a transaction that would advance the interests of both companies’ shareholders, employees and patients, as well as our country’s healthcare delivery system. We also call on Gentiva shareholders to make their voices heard by tendering their shares in support of Kindred’s value enhancing offer.”

Kindred noted the following:

• Kindred’s all-cash offer provides immediate and certain value to Gentiva’s shareholders at a time when Gentiva’s prospects are uncertain. Gentiva highlighted its pre-offer 52-week high stock price of $13.85, which it reached on August 14, 2013. Notably, this was before the market reflected a wide range of new concerns about Gentiva, including operational difficulties and integration challenges. In addition, the August 14, 2013 stock price does not reflect the material changes to home health reimbursement (“rebasing”) that became effective on January 1, 2014, nor does it account for significant reimbursement headwinds that Gentiva will face this year and for several years to come. As a multiple of EBITDA, our proposal represents a valuation greater than Gentiva has achieved on a standalone basis at any point during the last five years leading up to our offer.

• Kindred’s offer represents a 45% premium to Wall Street analysts’ unaffected one-year median price target of $10.00 per share. We believe that Gentiva based its recommendation to its shareholders on unsubstantiated projections that are inconsistent with the market’s assessment of Gentiva’s prospects. While Gentiva is using analyst estimates for its peers, it is asking its shareholders to trust management’s projections, which have been unreliable in the past, and which Wall Street does not believe are achievable.

• Kindred’s $14.50 per share cash offer values Gentiva at approximately 9.3 times research analysts’ 2014 EBITDA estimates. Gentiva’s public company peers trade at an average enterprise value of approximately 9.4 times research analysts’ 2014 EBITDA estimates. Discussions and appropriate due diligence would help determine any additional value to be delivered through Gentiva’s ‘One Gentiva’ plan.

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• Kindred is prepared to share the expected synergies with Gentiva shareholders through cash and stock consideration. Gentiva noted that its shareholders should also benefit from the synergies to be realized in the proposed combination. Kindred’s offer to include equity—which many Gentiva shareholders have told us they would prefer—would allow Gentiva shareholders to participate in the upside potential of the proposed combination.

Kindred believes its all-cash offer would deliver immediate and certain value that significantly exceeds what Gentiva shareholders could expect Gentiva to deliver on a standalone basis. The Kindred offer of $14.50 per share represents a 70% premium to Gentiva’s closing share price on May 14, 2014 (the day prior to Kindred making its proposal public) and a 64% premium over Gentiva’s 60-day volume-weighted average closing price on May 14, 2014.

In order to send a strong signal to the Gentiva board, Kindred continues to urge all Gentiva shareholders to tender their shares in support of its value enhancing offer. If a majority of the outstanding Gentiva shares are tendered prior to July 16, 2014, Kindred intends to amend the offer to seek to purchase 14.9% of Gentiva’s outstanding shares, positioning Kindred as Gentiva’s largest shareholder.

Forward-Looking Statements

This press release includes forward-looking statements including, but not limited to, statements regarding the Company’s ability to complete the Offering, the Company’s anticipated use of proceeds from the Offering, the tender offer for Gentiva common stock and the Company’s proposed business combination transaction with Gentiva (including financing of the proposed transaction and the benefits, results, effects and timing of a transaction), all statements regarding the Company’s (and the Company and Gentiva’s combined) expected future financial position, results of operations, cash flows, dividends, financing plans, business strategy, budgets, capital expenditures, competitive positions, growth opportunities, plans and objectives of management, and statements containing the words such as “anticipate,” “approximate,” “believe,” “plan,” “estimate,” “expect,” “project,” “could,” “would,” “should,” “will,” “intend,” “may,” “potential,” “upside,” and other similar expressions. Statements in this press release concerning the business outlook or future economic performance, anticipated profitability, revenues, expenses, dividends or other financial items, and product or services line growth of the Company (and the combined businesses of the Company and Gentiva), together with other statements that are not historical facts are forward-looking statements that are estimates reflecting the best judgment of the Company based upon currently available information.

Such forward-looking statements are inherently uncertain, and stockholders and other potential investors must recognize that actual results may differ materially from the Company’s expectations as a result of a variety of factors, including, without limitation, those discussed below, set forth in the Company’s Annual Report on Form 10-K and in its reports on Forms 10-Q and 8-K. Such forward-looking statements are based upon management’s current expectations and include known and unknown risks, uncertainties and other factors, many of which the Company is unable to predict or control, that may cause the Company’s actual results, performance or plans to differ materially from any future results, performance or plans expressed or implied by such forward-looking statements. These statements involve risks, uncertainties and other factors discussed below and detailed from time to time in the Company’s filings with the SEC.

Risks and uncertainties related to the tender offer and proposed transaction with Gentiva include, but are not limited to, uncertainty as to whether the Company will further pursue, enter into or consummate the offer or any transaction on the proposed terms or on other terms, potential adverse reactions or changes to business relationships resulting from the announcement or completion of the offer or any transaction, uncertainties as to the timing of the offer or any transaction, adverse effects on the Company’s stock price resulting from the announcement or consummation of the offer or any transaction or any failure to complete the offer or any transaction, competitive responses to the announcement or consummation of the offer or any transaction, the risk that regulatory, licensure or other approvals and financing required for the consummation of the offer or any transaction are not obtained or are obtained subject to terms and conditions that are not anticipated, costs and

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difficulties related to the integration of Gentiva’s businesses and operations with the Company’s businesses and operations, the inability to obtain, or delays in obtaining, cost savings and synergies from the offer or any transaction, uncertainties as to whether the consummation of the offer or any transaction will have the accretive effect on our earnings or cash flows that we expect, unexpected costs, liabilities, charges or expenses resulting from the offer or any transaction, litigation relating to the offer or any transaction, the inability to retain key personnel, and any changes in general economic and/or industry-specific conditions.

Many of these factors are beyond the Company’s control. The Company cautions investors that any forward-looking statements made by the Company are not guarantees of future performance. The Company disclaims any obligation to update any such factors or to announce publicly the results of any revisions to any of the forward-looking statements to reflect future events or developments.

Additional Information

This press release is provided for informational purposes only and does not constitute an offer to purchase or the solicitation of an offer to sell any securities of Gentiva. The solicitation and offer to buy Gentiva common stock have been made pursuant to an offer to purchase and related materials, as they may be amended from time to time. Investors and shareholders should read those filings carefully as they contain important information, including the terms and conditions of the offer. The offer to purchase and related materials, as well as Kindred’s other public filings, have been filed with the SEC and may be obtained without charge at the SEC’s website at www.sec.gov and at Kindred’s website at www.kindredhealthcare.com. The Offer to Purchase and related materials may also be obtained for free by contacting the information agent for the tender offer, D.F. King & Co., Inc. at (212) 269-5550 (collect) or (800) 859-8508 (toll-free) or by email at gentivaoffer@dfking.com.

About Kindred Healthcare

Kindred Healthcare, Inc., a top-150 private employer in the United States, is a FORTUNE 500 healthcare services company based in Louisville, Kentucky with annual revenues of $5 billion and approximately 63,000 employees in 47 states. At March 31, 2014, Kindred through its subsidiaries provided healthcare services in 2,313 locations, including 100 transitional care hospitals, five inpatient rehabilitation hospitals, 99 nursing centers, 22 sub-acute units, 157 Kindred at Home hospice, home health and non-medical home care locations, 105 inpatient rehabilitation units (hospital-based) and a contract rehabilitation services business, RehabCare, which served 1,825 non-affiliated facilities. Ranked as one of Fortune magazine’s Most Admired Healthcare Companies for six years in a row, Kindred’s mission is to promote healing, provide hope, preserve dignity and produce value for each patient, resident, family member, customer, employee and shareholder we serve. For more information, go to www.kindredhealthcare.com.

Contacts

Media Susan Moss Senior Vice President, Marketing and Communications Kindred Healthcare, Inc. 502-596-7296 or Andy Brimmer / Andrew Siegel Joele Frank, Wilkinson Brimmer Katcher 212-355-4449 Investors and Analysts Hank Robinson Senior Vice President, Tax and Treasurer Kindred Healthcare, Inc. 502-596-7732 or Jordan Kovler / Kristian Klein D.F. King & Co., Inc. 212-232-2247

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