Plastic gear in one of the headlight motors has stripped it's teeth, a fairly common C5 problem.
You can replace the gear with another plastic one, but most people opt to upgrade to a brass gear, which is a little more expensive (about $50), but should last forever.
Here are some sources for the brass gear...These are old pages, so you may want to email them first to confirm current availability:
Corvette C5 Headlight Motor Gears by Rodney Dickman
4th Generation Headlight Fix
I'm sure most of the usual Corvette parts places like Mid America, Corvette Central, etc also carry them.
If you Google "C5 headlight gear replacement", you'll find pages with pictures/instructions, also some how-to videos on Youtube on how to remove and disassemble the headlight motor.