Hi Phil,
iTunes doesn't require authorisation or de-authorisation. If you have the iTunes library and all content in place on the new drive just install iTunes fresh. It will find your stuff if it's in the default place, otherwise it can be shown where your stuff is. Login with your AppleID and you're done.
EDIT: it just clicked with me what you meant

Your AppleID can only be associated with five computers, therefore it is safest to de-authorise the old installation. If you forget that you can de-authorise all computers, then authorise the ones you're actually using.
Cheers
Steffen.