Authorization Deauthorization-What am I doing wrong?

I just bought two new mac minis replacing some older computers. I've ran out of authorization for my iTunes. So I deauthorized all my computers at once. I then authorized 1 computer. When I sign on, it notes it is the first of up to 5 that can be authorized. Then I try to play back a song. ITunes tells me it cannot play the song because I've already authorized 5 computers, even though seconds earlier it told me it was the only one. Can anyone help?