itunes doesn't recognise deauthorisation of devices

I have an itunes account. I have an Apple ID. I have apple devices. I have a sony device. I had my limit of 5 devices authorised -including the computer I wanted to play music on...

iTunes said I couldn't play my music (already paid for) because my computer WASN'T authorised - but according to my Apple account management page (opened on a browser) it was authorised.

Anyway, I proceeded to deauthorise an old iphone. Leaving me with FOUR authorised devices. Went to play music - same rigamarole, including can't authorise you on this computer because you already have 5 devices authorised. Quit itunes and browser. Restarted iTunes. NO CHANGE.

What do I have to do to get itunes to recognise deauthorisation of one or more devices? How can I get itunes to let me play music I have already paid for in the iTunes App?