How to authorize a Mac to play a movie

Years ago I purchased a few movies from within the TV app on a previous Mac. This year I purchased a new Mac, and I transferred my entire movie library from the old Mac to my new Mac. On the new Mac, when I try to play one of the movies, I get the message that I must authorize my computer. But when I try to authorize it, I get the message saying that I cannot authorize more than 5 computers.

So I went into TV > Account > Account Settings and deauthorized all computers. But when I try to play one of the movies, still get that same error, saying that I cannot authorize more than 5 computers.

Any suggestions on how to solve this?