I’ve lived in multiple countries, and wound up with multiple Apple IDs (because Apple insists on having unique email addresses per account, and one account per country, and one credit card on file per country too which must have a billing address in that country).
Each time I migrate machines, I deauthorize that computer, but it only seems to deauthorize the "dominant" (most recently used or default) account. The accounts from my other Apple IDs do not deauthorize.
I hit the 5-computer limit on one of these accounts, even though I only have (and only ever have) one computer at a time, and I attempt to deauthorize each time.
It turns out there is a nuclear option, which allows you to deauthorize all computers associated with a given Apple ID, although you can only do it once per year: