I ran into the issue that Xamarin won't activate and claims you have too many computers activated. The strange part in this is that it actually can activate the computer based on the Xamarin website, but XS just keeps whining about not succeeding.
Checking the logs in ~/Library/XamarinStudio-5.0/ revealed the problem: if you install both Xamarin.iOS and Xamarin.Android but only have a license available for one of these, Xamarin Studio will still try to get both and since it can't, it will just whine.
The proper way to work would be to say "sorry, I can't give you an Android license, but you can have this iOS license" and call it a day. That's it. But no, it's all or nothing.
So if you have this issue (or the other way around), you'll have to uninstall the other platform from your machine and then try activation.
This will happen even if you download the license file and try to do offline activation, since XS will still want to log you in.
Note that this might not happen to everyone. It may require having licenses for both platforms in unequal quantities when trying to log in.
Yet another reason to love Xamarin.