When I use my mobile data, my phone shows that it’s connected to 5G, but there’s almost always an exclamation mark, and I can’t use mobile data. Am I overlooking any settings? It’s for domestic use, so no roaming involved.
I’m using the Orange network
As a first pass, you could use
Settings > 
Search: Access Point Names
Try to tap top right menu on this APN page
“Restore default”.
I restored it and it looked fine for a couple of days. Now the problem reoccurs. Restoring the APN doesn’t fix it anymore.