Less than 5 hours is a little tight for this but it's the only one I know of for sure. Inlet Tower has a half-crew rate option for a partial day. ~$35+tax
They'll pick you up, 10 minute ride. You'll have to leave the hotel on the hour to head back to Fedex (that's the outbound van schedule).
Their # is (907) 276-0110

I know some guys use the Puffin Inn out by the airport but I don't know if they offer some kind of day room rate.

You could also try Northern B&B and see if Dorothy might be willing to hook you up with some kind of day room option. (907) 336-4248 She will pick you up and drop you off during normal day/night hours.

There are a few recliners in the jumpseat lounge if the above options don't work. Grab a pillow/blanket off the inbound flight because those usually aren't available in the lounge. You may want to call ANC ops and see if there's a locker room shower you might be able to use.