Authorizing new iMac for iTunes?

[lost in space]

I'm a baaaaaaad boy. I've been remiss about de-authorizing old computers for iTunes, and now it has caught up with me. I can't play some iTunes purchases on our new iMac because I'm over the limit of 5 computers. Some of that old iron left us years ago, so I'm considering de-authorizing all, then authorizing the three computers we sill have. Two of them would be re-authorized. Is this a good approach? Are there any downsides?

Thx