5 month old baby started waking lots through the night?

Do not start feeding him again at 4 am or he'll get used to it and you'll be stuck doing that for a good while. He is probably waking due to teething. You could rub a little orajel on his gums and soothe him briefly and then let him fall back asleep. He may not like it at first, but letting him self soothe will benefit you both in the long run. As long as he doesn't have a fever, too, he'll fall back asleep. Also, maybe he needs a tad more to eat just before bed to fill him up a bit more. He could be having a growth spurt and just need a little more in his tummy. Good luck!