My DS is exactly the same. I don't want to scare you but he started the 2 hourly wake ups at about 13 weeks, 7 weeks later it's still going on, though I think getting slightly better. He will also have quite a good chunk of sleep at first, then wakes gradually more frequently. I would also maybe put your DS to bed a bit later, then it doesn't seem like he wakes up as often! My DS is usually asleep 8.30 - 9ish, then wakes 2 or 3 times for a feed then up for the day at 7am. But if your DS is getting up at 5.30am I would definitely be going to bed with him for that first longer stretch of sleep ( if you can, I know it's tempting to use that time to get things done and to eat, shower etc! )
I was advised by a bf counsellor to feed him every time he wakes as he will be hungry. A couple of times if it's been less than say an hour and a half since the last feed I've managed to settle him without, but tbh if you're up anyway you might as well feed!
Was also advised to give baby rice, though think my HV is slightly more sensible, she said start to introduce it at 20 weeks just once a day at lunchtime as putting them to bed with a full tummy can be counter productive. I haven't given it yet though, we've got this far we might as well wait another few weeks!
I wouldn't bother with formula, I did try this once out of curiosity. He did sleep better, ( 6 hours, then 1.5, then 3 ) but then he didn't poo for 2 days and when he did it was vile! I also felt guilty so haven't given it since.
Definitely look up 4 month sleep regression on here, there are so many people going through the same thing! I found it really helped to know that its both normal and common, as I felt like I must be doing something wrong! No doubt someone will tell you that you are Making A Rod For Your Own Back and someone else will probably tell you to give him water!! Ignore them and hang on in there. It will get better. Apparently..... :)