One month old naps

A

My son will be 5 weeks on Thursday and starting at around the 2.5 week mark he starting taking very short naps. He takes maybe two 30 minute naps total during the day. Once he is up its very hard to get him to fall back asleep. At night once he falls asleep he will wake two sometimes 3 times which is fine but during the day I cant get anything done. Is this normal?