If your Mac gets a new logic board you’ll find that many of your software licenses must be re-applied or re-activated. For example, iTunes wouldn’t recognize my newly repaired MacBook Pro as being authorized.
My former authorization was orphaned and iTunes doesn’t allow its removal. Being forced to re-authorize used another one of my five precious authorizations…putting me at four. I began to wonder the consequence of orphaned authorizations but fortunately Apple has solutions for this.
If you reach the maximum of five authorized computers you can use the “deauthorize all” option in iTunes which resets the count back to zero. At that point you can authorize your primary computer and whatever others you wish. This can be done once per year.
Read the iTunes Authorization FAQ for everything you ever wanted to know.