The 5th Generation iPod is particularly finicky and troublesome to diagnose. I would definitely advise looking over the iPod 5th Generation troubleshooting page first.
Having that said, I have seen up to 100 GB hard drives for the iPod 5th Generation (check Google for an example). These specialty hard drives are quite expensive! It's a toss-up of whether or not it is more cost-effective to purchase a new iPod.
HOWEVER, you don't want to just add your iPod to a landfill!!! If just the hard drive is broken, consider replacing it with a discount 60 or 80 GB hard drive and making it a Christmas gift?