I smiled reading this OP. I had (and was myself) an early riser.
Some of this is genetic we know there are "early genes" and "late genes" so to some extent it's inate. There are 2 issues here;
First is; "how do I prevent my child waking up before I am ready to start the day"
Second is "what can I do to make the 5am wake up bearable?"
So lying queitly in the dark (as PP) says giving the message nothing interesting happens before 6 or 6:30- or whatever you decide, might tick both boxes.
Being firm and putting him back to bed to listen to the crying , might teach him to go back to sleep, but does not improve your life in that moment.
Other things that help with early waking are;
a shorter morning nap (IME this really works) no more than 1 sleep cycle (45 minutes) before noon which should'nt be before 9 or one nap at 11 or 12 which lasts a couple of hours. Then a "cat nap" at 4pm for 20mins.
As others have said being too tired at bed time makes early waking worse this is exacerbated by a long morning nap. I did this a few times when things got bad, it took commitmant and some difficult days but worked to some extent.
Of course you can go the other way and accept it as your lot in life, get up clean the house, put the telly on or a I did start crafts and baking- unfortunately that definately sends the message it is morning and playtime and will entrench the early start.
FWIW in retrospect I didn't try hard enough with the first strategy and "gave in" to starting my day super early too much. I would also say as an early waker myself (with an early waking DM- as I said it's genetic) that learning to lie quietly in the small hours waiting for sleep to come is a good skill to aqquire young.
Sorry for the essay good luck. I don't think there is an easy answer.