Baby waking at 5am every day

For the past couple of weeks my 4 week old has started waking a 5am without fail. It doesn't matter how recently he had a feed, even if I know he's not hungry, he will still wake.

We've tried leaving him to see if he will settle but eventually he will start to cry. We've tried settling him ourselves but nothing works

So eventually we end up taking him downstairs and either holding him in our arms (where he will sleep) or put him in his swing where he will sleep for a bit too

I really don't know why he wakes at this time everyday but will go back to sleep downstairs?? 

Help!