Hi
This may not be very helpful to you but I'm experiencing exactly the same thing! My 19 week old (just over 4 months) has started waking at 5AM exactly every day.
He's never slept through but hasn't been a bad sleeper and we could always get him to go back to sleep until later until recently.
I've spoken with the health visitors who suggested ? it was time to wean - but I want to wait longer and with my DS there are no other signs such as being unsatisfied with etc.
I am BF but give a bottle of formula at night and the HV also suggested trying Aptimil milk for hungry babies but this has made no difference for us - might be also worth a try though.
Also, dream feeding before bed - again made no difference to us but might be worth trying before you go to bed if you haven't already.
I wondered whether his poor daytime napping may affect things too? He naps for 1/2 hour around 9AM, sometimes another 1/2 later morn and then an hour in the aft max - no matter what I do, in or out, car seat etc, can't get him to have any more. They say, good daytime naps help nigh time sleep.
Also, when we put him to bed he often falls asleep feeding and I thought maybe this wasn't great as it wasn't teaching him how to go to sleep himself in the cot so when he wakes at 5AM (apparently around this time is baby's lightest sleeping time), he can't get himself back to sleep. So, we've started putting him to bed earlier - about 6-7, to try and help him go down awake. He cries for 10 mins or so and then goes off fine, but is still waking at 5 at the mo, but intend on carrying this on for a few more days. Might be worth trying if you have similar problems?
This morning I did feed him and he did go back off, but like you - I'm sure he wasn't hungry and I'm mindful of feeding for comfort creating problems later on. Also, this doesn't fit with the E.A.S.Y method which I sort of try and stick to.