I am migrating a server in 10 days which is currently running Virtualmin Pro on Debian 5.0 x64.
I would like to know if the backups will successfully restore on a system with Debian 6.0 x64 on it, or if I need to dist-upgrade the old system prior to migration.
It should be no problem to restore your backups onto your new server.
In general, backups can be restored from one distro to another with minimal problems. In your case, going from Debian 5 to 6, there’s minimal changes there, and you should be just fine.
You’d of course want to be prepared for things to go awry, and even do some testing before making the new server live – just in case