Some toddlers dont even sleep through the night!
I think (without sounding harsh) that you should accept that this is what life with a baby is like. He is only 5 weeks old, and his routine will be all over the place, as expected. There is nothing that you can do that will make him sleep through the night, he will when he is ready.

Having said though, there are things that you can try to encourage him to go to bed at a later time, this would mean working on his day routine too, as well as night routine. Shifting day sleeps, or holding them off even for 10 mins if you can. I cant really help in that aspect coz til about 9mths old I pretty much went with my babys lead!

Trust me, I know its not easy with a new little bub! Its a bit of a shock to the system, and you do want to spend the time you have with your hubby, but the saying "Sleep when the baby sleeps" pretty much explains itself.