So you didn't answer my question about any recently installed apps. Also since both are affected, did they perhaps get a firmware update just before this started? What is your carrier and the exact model S5? There might be more information for you in the forum for your carrier regarding updates and resulting phone problems people have experienced.
If this is related to an update, it may help to clear the cache partition from the recovery menu, or to do a full factory reset (of course be sure your personal data is backed up first). A reset often resolves problems like this that happen after an update.
Also one thing you can try first that is easy is a battery pull. Take the back off the phone, remove the battery and leave it out for a few minutes, then put it back in and turn on the phone. See if the drain problem still exists after that, you might get lucky and that's all it takes to fix it. If it still happens then you'll need to look further.