B.
Sounds like a normal baby to me he's only 5 weeks old he's not supposed to sleep through the night those that do are the odd ones. Try feeding him when he first wakes up instead of waiting. You will all get better sleep if you don't let him cry, feed him then go back to sleep. His little tummy is only as big as his fist and they digest food very quickly , they are growing very quickly.
relax and accept that babies wake and need to be fed at night. anyone that tells you different is crazy or lying. I had one that needed to be fed every few hrs until she was a yr old, but then I had one that only needed one feeding in the middle of the night at 10 months old then dropped it all together on his own at a year. They are all different and some need more love , cuddles , food , etc than others.