Hi Marie,
Good work!
OK, so here's some things I'm thinking and some things I've been told.
If they wake up, and you are able to get them back to sleep, and then they wake up within the hour, *that's* hunger. So when he woke at nine, and then woke again at ten, and you fed him, that's correct. Same with the 12:30 and the 1:30. So he may be going through a GS. He's almost six months old, right?
There are two ways that I can think of off the top of my head to tell if you are making enough milk. I don't know where you are, what country or state, but here in San Diego they have breastfeeding "clinics" where you can take your LO, weigh him, breastfeed him, and then weigh him afterwards to see how much he took. These clinics are free and provide that service.
The other way you can do it (since he takes a bottle) is to pump for one day and only feed him EBM so you can actually see how many ounces he is taking. For example, you would normally BF him at 7 - so give him a bottle of EBM and then double pump as soon as you can after/as close as it would be to the normal BF. He would be able to extract about an ounce more from your breasts than you'll be able to pump, so you would calculate that. Does that make sense?
So instead of BFing, you give him a big bottle of EBM - say six oz (since he's proven that he can drink 5.5 in the middle of the night). If he drains it, it means he needs to eat more, if he leaves some it means he needs less. And then pump and see how much you get. So let's say you get 5 oz pumped, then he would probably be able to drain 6oz from your breast, and you could calculate from there (drank 7 oz of EBM, only pumped 4oz - 2oz deficit, etc.) It's not an exact science, but it's a ball park.
If you find there is a deficit, then you can work on ways to up your supply - feeding him more often, feeding him both breasts, drinking Mother's Milk Tea, etc.
And by the way, if he drank ten ounces at night, that's a lot of food! We need him to start eating that during the day! To answer the title of your post, I would say your LO is hungry. And of course the reason he's not eating more during the day is b/c he's drinking so much at night. So we would slowly work on getting him to eat more during the day and eliminating the 1/2/3am feeding and the 5am feeding.
I will also say it's very normal for a five month old, especially a BF baby, to still need to eat at night. So don't beat yourself up about that. What we want to do is have him only wake to eat. Not wake, resettle, wake, resettle, wake, eat, resettle and repeat.
Do you give him both breasts during the day at every feed? You said you think he can go four hours between feedings. It will be interesting to see if he can.
Let me know what you think and how it goes!
Lu