11 hours is a long time to go without milk for a 5-month old, so sounds like you're doing really well actually! It may be that his system just needs milk again at that time, regardless of whether you try to feed him earlier.

With time you may find that your DS will push his bed time back a bit later and maybe even stretch that sleep out so you get a more reasonable wake-up time. I wouldn't necessarily expect solids to do that. If you want to try pushing back the bed time just be careful, because you can stuff things up if you mess with their system. (we tried it at one point as DS was waking around 5am and he actually started waking up even earlier )

My DS is over 2 and still can't sleep longer than 11 hours total (sometimes that's all at once) and he's starving come morning (and he even has midnight snacks sometimes too!).

Give it a little time