Is it a domain account or one local to the computer?
Sounds like it's trying to contact a domain controller to verify your password, which it can't do ofc. since you're not on the school network. After a timeout it should give up trying to contact the DC and instead check the password against cached credentials, provided you've logged in to that machine at least once already using the same password.
5 minutes seems like a long time, though. I think there's a long delay if you try to login to an account that is locked-out, in order to reduce the opportunity for brute-forcing passwords. Not sure exactly how that works these days, though.