Why does my iPhone 5 say that I've used it for a few hours, when in reality I've only used it for a few minutes?
Check your charging cord. The "time since last full charge" implies it was taken off charge that many hours ago. Possibly because the charging cable became disconnected or is failing.

Then of course you can try a factory reset of the phone, after a full backup. If it works then try restoring from your backup. I know this can be a bit of trouble.

But honestly an iPhone 5 battery, if original, is likely to be at the end of its life. Try replacing the battery before getting rid if the phone.