Q: After I search the top 5 cards. Do I shuffle any cards did not choose back into my deck?

A: Yes. Anytime you "Search", you always shuffle. -(Developer Ruling)

So…in the past, I made a mistake. I said before that no, you do not shuffle. But Caleb and I have talked very recently. And we decided that anytime you search, you always shuffle. We will update the rules reference eventually…to make it that you always shuffle. – Boggs

One really cool thing about this card is that unlike Jessica Drew's Apartment, it doesn't make you shuffle your deck afterwards. Once Hawkeye has this in play, he'll always know what he's getting from Avengers Mansion or Press the Advantage, which can be a big help in turn planning, and he'll also have a good deal of information about his upcoming hand.

This potentially makes it much easier for Hawkeye to take advantage of the various events that are meant to be played during the villain phase. Foiled! is an incredibly efficient card if you happen to be in alter-ego when you draw it, but sometimes it's too risky to flip to your alter-ego if you don't know whether you'll draw it. If you stay hero and do draw it, then holding it in your hand for an extra turn effectively doubles its cost. Fortunately, with Hawkeye's Quiver you can stay in hero form until you know you're about to draw Foiled!, and time your flips accordingly.

There are some heroes that play completely differently while they have a card from their kit in play vs not in play. Hawkeye with Hawkeye's Quiver is a prime example. Hawkeye's main problem lies in the fact that his Arrow events are what make him good, but his hero ability does nothing other than help you play your Arrow events, so his power level is up to the luck of the draw even more than most heroes. If you don't draw any Arrow events, then you might as well be playing with a blank identity; and if you draw too many of them, you'll just be spending them to pay for each other. But Hawkeye's Quiver solves both of those problems at once: you get to look for an Arrow event every turn you're in hero form, and you get to hang onto them separately from your hand for as long as you need until you play them. Overall a 100% high priority card to get into play any time you see it in your hand.