Exhibit E

Form of Letter from the Fund to Shareholders in

Connection with Acceptance of Offers of Tender

Eagle Point Institutional Income Fund

[   ], 2023

Dear Shareholder:

Eagle Point Institutional Income Fund (the “Fund”) has received your tender of all or some, as the case may be, of your shares of beneficial interest in the Fund (the “Shares”). The Fund accepts your tender in its entirety, subject to the following sentence. In the event that the amount of Shares collectively tendered by all Shareholders pursuant to the tender offer which commenced on May 31, 2023 (the “Offer”) exceeds the maximum number of Shares which may be purchased by the Fund under the terms of the Offer (determined, in accordance with the terms of the Offer, as of May 31, 2023) (the “Maximum Purchasable”), the Fund will proportionately reduce the value of each tendering Shareholder’s tender such that no more than the Maximum Purchasable will be purchased by the Fund, and the Fund accepts your tender as so proportionately reduced.

In respect of the Fund’s purchase of all or some, as the case may be, of your Shares (the “Repurchased Shares”), as described above, you are entitled to receive a payment, to be paid in cash, in an amount equal to the value of your Repurchased Shares based on the net asset value of the Fund as of June 30, 2023, in accordance with the terms of the Offer. In the event that you have tendered only some (but not all) of your Shares, the value of your remaining Shares must be equal to or greater than the required minimum amount of $2,500 (in accordance with the terms of the Offer). Provided that the value of your Shares does retain, at the least, this required minimum amount, cash in the amount of the payment due will be wire-transferred as soon as possible following June 30, 2023, unless the valuation date of the Shares in the Fund has changed or the Fund has requested a withdrawal of its capital from the Fund’s investments. If you tender an amount that would cause your remaining Shares to fall below the required minimum of $2,500, the Fund reserves the right to repurchase or redeem all of your Shares at any time if the aggregate value of your Shares is, at the time of such compulsory repurchase or redemption, less than $2,500.

You remain a Shareholder of the Fund with respect to any of the Shares which the Fund is not purchasing pursuant to this Offer.

Should you have any questions, please feel free to contact one of our dedicated account representatives at (866) 661-6615, Monday through Friday (except holidays), from 8:00 a.m. to 6:00 p.m., Eastern time.

Sincerely,

Eagle Point Institutional Income Fund

Enclosure

Note: Eagle Point Credit Management LLC does not render advice on tax and tax accounting matters to clients. This material is not intended or written to be used, and it cannot be used, with any taxpayer for the purpose of avoiding penalties which may be imposed on the taxpayer under U.S. federal tax laws. Federal and state tax laws are complex and constantly changing. You should always consult your legal or tax advisor for information concerning your individual situation.

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