By sleeping

Hi,

How old is he? And what kind of food is he eating?

I think 5 weeks and sleeping through the night is still a bit early. Our daughter slept 6 hours straight after 8 to 9 weeks, and apparently that's already quite fast. She was feeding 6 times a day then.
Good luck!

At 5 weeks, sleeping through the night is often not really a thing yet. Of course, there are babies who do sleep through the night..
In a few weeks, you'll see that a different rhythm will emerge You can always ask at the health center if the amount of bottle feeding is sufficient. Good luck!

It's totally normal for a 5-week-old baby not to sleep through the night. Our twins are now 6.5 months old and generally sleep well, but not every night is the same. Sometimes they keep us wide awake.

Still way too young for sleeping through the night. Sleeping through is really a luxury. I have 4 kids, and none of them are sleeping through yet. They're 16, 14, 6, and 4 years old. For the youngest 2, we still have to get up regularly. The oldest 2 are managing on their own now, thankfully.

I myself never sleep through either.

As long as your baby needs you, they'll come. Every 3 hours at 5 weeks is actually quite normal. Nights are the hardest. Lots of strength. Don't let yourself get worked up by stories about sleeping through.