Whoops, sorry I missed this!
Does he take a pacifier/soother/dummy? If so, will he accept that in place of the 5AM feed?
If he's still looking to feed then, I'd go ahead and do it for now, maybe not switch up TOO many things at once, but also try to increase daytime calories, see if he'll get to a place where he doesn't need that extra feed when he should be sleeping. What's his activity level like when he's awake? Getting lots of tummy time? That burns up calories like crazy, but so SO good for neuromuscular development!