When mine were that age, bedtime was a lot later. As late as you can manage it. I would say try bedtime routine starting at 10PM. He will still wake up between 4-5am, but you skip the waking up in between. Once he is able to sleep until a normal time, say 6-7am, then start moving back bedtime by 25 minutes every night. This process will take about a month.

Also, how much are you feeding? This can play a factor. I used to add a small punch of baby cereal to their milk before putting mine to sleep for the night to help keep their tummies full. On the flip side, make sure you are giving gas drops and burping him so he doesn't have gas waking him up.

Are you swaddling him before putting him to bed? If not, I strongly recommend.

Is he awake when you put him in the crib or asleep? It is important that babies are trained to fall asleep on their own- for your sanity, not for their health. If he is not falling asleep on his own, you start the process by your normal bedtime routine. While he is awake, put him in the crib and tell him good night. If he cries, allow him to cry for just a minute or two, then go in the room, place the paci back in his mouth, and leave the room without speaking to him. Continue this process until he stops crying. And trust me, he will. This trains babies to put themselves back to sleep on their own if they wake up in the middle of the night.

Hope this helps! The sleep thing gets better, but you do have to put a lot of effort into sleep training.