3 month old waking at 5am everyday screaming

[Hamnvik]

My ds is 13 weeks and has woken up at 5am everyday since he was 3 weeks old. I watch him in his cot and can see him stirring but his legs seems to kick about and stop him from settling until he gets annoyed and starts crying.
I thought it was him trying to poo but he doesn't go until about 10am. He won't eat when he wakes at 5 he just cries and kicks his legs. Could it be wind at the same time everyday? I've tried winding him when he wakes up but I can never get him to burp.
I can usually get him back to sleep by 7 but he only sleeps for 30mins max but wakes up quite happy.
He has reflux as well but I'm not sure its related to that? Can babies get restless legs? Help, I'm so tired of rocking a screaming baby at 5am everyday!