Laptop power supply trouble?

No.

If its running the os shuts itself down at like 5%.

Assuming nothing was in the process of being written at the exact instant that power cut out nothing would be harmed. Windows will be fine and many drives have write protection these days so its highly unlikely that anything will have been harmed.

so what if i leave my laptop unplugged and the battery drains out completely what happens to the hard drive and the files inside?

The hard drive is non volatile unlike ram, a hard disk doesn't need a constant stream of power to maintain the data on it, they are stored on magnetized disks which will hold their data for a few years without any need to power up the drive. You could take the drive out and leave it on the table for a year and it wouldn't affect the files inside.