Q: itunes doesn't transfer bought apps

ok, i'm on 10.10.3 and itunes 12.1.2

I bought a flashcard app a while ago, and when I wanted to update, and sync I get a msg saying that the ipad mini couldn't be synced, cause the computer isn't authorized anymore for the bought items. Adding I have to authorize this computer.

So I did from the menu, I'm getting : this computer is one of five autorized.

But I'm still getting the same error msg when syncing, even when relaunching itunes and rebooting...

I don't remember whether I bought the app with another apple ID, but I'm quite lost now as how to get the app working...

Thanks for any help