Exhibit (a)(1)(E)

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

AdvancePierre Foods Holdings, Inc.

at

$40.25 Net per Share

Pursuant to the Offer to Purchase Dated May 9, 2017

by

DVB Merger Sub, Inc.

a wholly owned subsidiary of

Tyson Foods, Inc.

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF THE DAY ON JUNE 6, 2017, UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED (SUCH DATE AND TIME, AS IT MAY BE EXTENDED, THE “EXPIRATION DATE”).

To Our Clients:

Enclosed for your consideration are the Offer to Purchase dated May 9, 2017 (as it may be amended or supplemented from time to time, the “Offer to Purchase”) and the related Letter of Transmittal (as it may be amended or supplemented from time to time, the “Letter of Transmittal” and, together with the Offer to Purchase, collectively the “Offer”) in connection with the offer by DVB Merger Sub, Inc., a Delaware corporation (“Purchaser”) that is a wholly owned subsidiary of Tyson Foods, Inc., a Delaware corporation (“Parent”), to purchase all outstanding shares of common stock, par value $0.01 per share (the “Shares”), of AdvancePierre Foods Holdings, Inc., a Delaware corporation (“AdvancePierre”), for $40.25 per Share (the “Offer Price”), in cash, without interest, subject to any withholding of taxes required by applicable law and upon the terms and subject to the conditions set forth in the Offer. Also enclosed is AdvancePierre’s Solicitation/Recommendation Statement on Schedule 14D-9.

We or our nominees are the holder of record of Shares held for your account. A tender of such Shares can be made only by us or our nominees as the holder of record and pursuant to your instructions. The enclosed Letter of Transmittal is furnished to you for your information only and cannot be used by you to tender Shares held by us or our nominees for your account.

We request instructions as to whether you wish us to tender any or all of the Shares held by us or our nominees for your account, upon the terms and subject to the conditions set forth in the Offer.

Your attention is directed to the following:

1. The Offer Price is $40.25 per Share, net to the seller in cash, without interest, subject to any required withholding of taxes and upon the terms and subject to the conditions set forth in the Offer.

2. The Offer is being made for all outstanding Shares.

3. The Offer is being made pursuant to the Agreement and Plan of Merger, dated as of April 25, 2017 (as amended from time to time, the “Merger Agreement”), among AdvancePierre, Parent and Purchaser. The Merger Agreement provides, among other things, that as soon as practicable (and in any event within two business days) after consummation of the Offer and subject to the satisfaction or waiver of the other conditions set forth in the Merger Agreement, Purchaser will merge with and into AdvancePierre (the “Merger”), without a vote of the stockholders of AdvancePierre in accordance with Section 251(h) of the General Corporation Law of the State of Delaware (the “DGCL”) with AdvancePierre continuing as the surviving corporation and a wholly owned subsidiary of Parent. At the effective time of the Merger, each outstanding Share (other than (i) Shares owned by Parent, Purchaser, AdvancePierre (or held in AdvancePierre’s treasury) or any direct or indirect wholly-owned

subsidiary of Parent or AdvancePierre immediately prior to the effective time of the Merger, or (ii) Shares held by any stockholder that has properly exercised appraisal rights under the DGCL) will be converted into the right to receive the Offer Price in cash and without interest, less any required withholding of taxes. No appraisal rights are available in connection with the Offer. However, if the Merger is consummated, pursuant to the DGCL, stockholders who do not tender their Shares in the Offer will have the right, by fully complying with the applicable provisions of Section 262 of the DGCL, to choose not to accept the consideration payable for their Shares pursuant to the Merger, and instead to demand an appraisal of their Shares by the Court of Chancery of the State of Delaware and to receive a cash payment of the “fair value” of their Shares as of the effective time of the Merger as determined by the Court of Chancery of the State of Delaware. The “fair value” of such Shares may be more than, less than, or equal to the Offer Price. The Merger Agreement is more fully described in Section 13 of the Offer to Purchase and stockholders’ appraisal rights are more fully described in Section 12 to the Offer to Purchase.

4. The AdvancePierre board of directors (the “AdvancePierre Board”) has unanimously (i) determined that the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger, are fair to and in the best interests of AdvancePierre and its stockholders, (ii) approved, adopted and declared advisable the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger, in accordance with the requirements of the DGCL, (iii) resolved that the Merger Agreement and the Merger shall be governed by Section 251(h) of the DGCL and that the Merger shall be consummated as soon as practicable following the time Purchaser first accepts for payment Shares validly tendered and not withdrawn pursuant to the Offer and (iv) resolved, subject to certain terms set forth in the Merger Agreement, to recommend that the stockholders of AdvancePierre tender their Shares into the Offer.

5. The Offer and withdrawal rights expire at 12:00 midnight, New York City time, at the end of the day on June 6, 2017, unless the Offer is extended or earlier terminated (as it may be extended or earlier terminated, the “Expiration Date”).

6. The Offer is conditioned upon, among other things, there being validly tendered in accordance with the terms of the Offer and not validly withdrawn, immediately prior to the expiration of the Offer, a number of Shares (excluding any Shares that have not been “received” (as defined in Section 251(h) of the DGCL)) that, together with the Shares owned by Parent, Purchaser and any other direct or indirect wholly-owned subsidiary of Parent, represents at least a majority of the Shares then outstanding on a fully-diluted basis as of the date and time at which the acceptance for payment of Shares pursuant to and subject to the Offer occurs and (ii) the expiration or termination of any applicable waiting period (and any extension thereof) under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended, without the imposition of a “Burdensome Condition” (as described in more detail in Section 16 of the Offer to Purchase). There is no financing condition to the Offer. These and other conditions to the Offer are described in Sections 15 and 16 of the Offer to Purchase.

7. No alternative, conditional or contingent tenders will be accepted. In all cases, payment for Shares accepted for payment pursuant to the Offer will only be made after timely receipt by the Depositary of (i) certificates evidencing such Shares or confirmation of a book-entry transfer of such Shares into the Depositary’s account at The Depository Trust Company pursuant to the procedures set forth in the Offer to Purchase, (ii) the Letter of Transmittal, properly completed and duly executed, with any required signature guarantees or, in the case of Shares held of record in book-entry form by a clearing corporation as nominee, an Agent’s Message (as described in the Offer to Purchase) in lieu of the Letter of Transmittal and (iii) any other documents required by the Letter of Transmittal. Accordingly, tendering stockholders may be paid at different times depending upon when certificates or book-entry confirmations with respect to Shares are actually received by the Depositary. If you wish to tender Shares pursuant to the Offer and cannot deliver such Shares and all other required documents to the Depositary or cannot comply with the procedures for book-entry transfer described in Section 3 of the Offer to Purchase, in each case prior to the Expiration Date, you may nevertheless tender such Shares by following the procedures for guaranteed delivery set forth in Section 3 of the Offer to Purchase.

8. Any stock transfer taxes applicable to the sale of Shares to the Purchaser pursuant to the Offer will be paid by the Purchaser, except as otherwise set forth in Instruction 6 of the Letter of Transmittal. However, federal income tax backup withholding at a rate of 28% may be required, unless the required taxpayer identification information is provided and certain certification requirements are met, or unless an exemption is established. See Instruction 8 of the Letter of Transmittal.

If you wish to have us or our nominees tender any or all of your Shares, please complete, sign, detach and return the instruction form below. An envelope to return your instructions to us is enclosed. If you authorize tender of your Shares, all such Shares will be tendered unless otherwise specified on the instruction form. Your prompt action is requested. Your instructions should be forwarded to us in ample time to permit us to submit a tender on your behalf by the Expiration Date.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the laws of such jurisdiction. In those jurisdictions where the applicable laws require that the Offer be made by a licensed broker or dealer, the Offer will be deemed to be made on behalf of Purchaser by American Stock Transfer & Trust Company, LLC or one or more registered brokers or dealers licensed under the laws of such jurisdictions to be designated by Purchaser.

Instruction Form with Respect to

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

AdvancePierre Foods Holdings, Inc.

at

$40.25 Net per Share

Pursuant to the Offer to Purchase Dated May 9, 2017

by

DVB Merger Sub, Inc.

a wholly owned subsidiary of

Tyson Foods, Inc.

The undersigned acknowledge(s) receipt of your letter and the enclosed Offer to Purchase dated May 9, 2017 and the related Letter of Transmittal (collectively, as may be amended or supplemented from time to time, the “Offer”), in connection with the offer by DVB Merger Sub, Inc., a Delaware corporation (“Purchaser”) that is a wholly owned subsidiary of Tyson Foods, Inc., a Delaware corporation (“Parent”), to purchase all outstanding shares of common stock, par value $0.01 per share (the “Shares”), of AdvancePierre Foods Holdings, Inc., a Delaware corporation (“AdvancePierre”), at a purchase price of $40.25 per Share, net to the seller in cash, without interest, subject to any required withholding and upon the terms and subject to the conditions set forth in the Offer.

The undersigned hereby instruct(s) you to tender to Purchaser the number of Shares indicated below (or if no number is indicated below, all Shares) held by you or your nominees for the account of the undersigned, upon the terms and subject to the conditions set forth in the Offer furnished to the undersigned. The undersigned understands and acknowledges that all questions as to the validity, form and eligibility (including time of receipt) and acceptance for payment of any tender of Shares made on my behalf will be determined by Purchaser in its sole discretion.

The method of delivery of this Instruction Form is at the election and risk of the tendering stockholder. This Instruction Form should be delivered to us in ample time to permit us to submit the tender on your behalf prior to the expiration of the Offer.

Number of Shares to be Tendered:

                                                                       Shares^*

Dated                                                              , 20    

SIGN HERE

Signature(s)

Name(s) (Please Print)

Address(es)

(Zip Code)

Area Code and Telephone Number

Taxpayer Identification or Social Security Number

^*  Unless otherwise indicated, it will be assumed that all Shares held for the undersigned’s account are to be tendered.