One of the nurses at our unit gave me the best advice ever. Up, fed, back down in 30-45 minutes tops. After this they will burn more calories than they have taken.
Of course it depends on how long it takes to feed them but I found I would get about 10-15 minutes of "playtime" after a feed and change. Then she would sleep for 2-3 hours. It was frustrating as I always just wanted to get her up for a cuddle. Of course, as time went on, I began to quite like the fact I had 2 or 3 straight hours where I could get on with things that needed doing or catch up on my sleep. Now she's up for longer and down for less, there aren't enough hours in the day!
Abby was kind of the same with her last "night" feed and it was the one I was most tired at. If you are breastfeeding, try taking him into bed and feeding him lying down. Occasionally we would both end up falling asleep, but I always made sure everything was arranged so she was safe. But most of the time I could pop her back in her basket with the minimum of movement and she generally stayed asleep. The main problem came when it was quite chilly, putting her into a cold basket would wake her up so we would either pop a hot water bottle in there to keep it cosy whilst she was feeding, or feed her wrapped in a blanket which she would then be laying down on.
I also would feed her lying on the sofa occasionally during the day, that way I'd get a nice long cuddle while she slept! (Our sofa is extra wide so we both had plenty room)
If it's any consolation, she eventually moved her 5am to a 7am and it was much easier to deal with!