If he's not crying or upset, I suggest just leaving him, 5am seems to be quiet a normal time for babies to wake up (unfortunately) & if you do too much you just reinforce it, but leaving him, it may soon stop.
Also funnily enough more day sleep can actually stop it... I get 5am wakeups from my 4.5mo (& 2yo) if he has a day with too little sleep or they go to bed too late.
what does an average day look like?