What causes the battery to drain on a 2003 Mitsubishi Galant after the car is shut off for greater than 5 hours?

A short somewhere along your electrical system.

Or a faulty battery.

Next time you come in from a drive, disconnect your battery from the car, leave it off for greater than 5 hours.

Then re-connect your battery after 5hrs time and see if the car will start.

If the car starts then your battery is OK and you will have to trace the short in your electrical system.

If the car doesn't start then buy a new battery and you're good to go.