Baby fighting sleep

My LO is nearly 5 weeks corrected age (was born 31+5 GA). Lately I’m having trouble settling him for a nap, especially in the morning. He will wake at 5ish to feed and won’t sleep for hours on end. I’ve tried leaving him on the play mat with high contrast pictures to look at which he seems to like, rocking him in the swing chair, in his pram, holding him… he is eventually gets tired but won’t fall asleep and starts getting fussy. He won’t take any more milk, so he’s not hungry. Any other ideas?