Can 37-622 tyres replace 32-622 tyres?
You'll probably have lots of room. Mountain bike frames generally have lots of room in the fork and stays for various sized tires. But it would be best to measure it.

The supposed size difference in your tires is 5 mm, so hypothetically you would need more than 2.5 mm of clearance on either side between the tires and the forks on the front and back of the bike. However, you will absolutely want more than this amount of clearance for several reasons.


advertised tire widths are not necessarily accurate. It could easily be off by a milimeter or two. Especially if one tire is lugged and the other is not.
Tires will move around a little when you are riding. If it's only clearing the fork / stays by 1mm in the stand, it will definitely make contact occasionally while riding.
If you have fenders, be very wary. Fenders are often designed to only fit a certain tire size. Be extra careful measuring clearances here.


So I would only recommend investing in the sidegrade if you have 1cm clearance right now, or more.

As a more general answer for this question to others seeking similar information, you should also check that the brake arms will clear a wider tire. It shouldn't usually be a problem with cantilever brakes, but with calipers a wider tire is often not going to fit. It's not an issue for Hugo because he is running disc brakes.