I know the batteries for the drone need to be discharged if not used for 10 days or more. But what about the controller?

I usually just discharge after five days. Not sure what is best.

Yes, it's the same for the controller. It's not easy to discharge the battery either (unless you have Android where it can be used to charge). You can't just leave it on to run down the battery, it starts beeping after a minute or two.