I agree with everything Arizoni and Singhg5 said, except I'd like to add that since they both ride G5 models, which has different-shaped engine side covers than the C5 and B5 models, they wouldn't necessarily know that on these models it's actually quite easy to feed a new chain over the drive sprocket on its own.
When I was sorting out a chain problem, I removed and installed the chain this way many times in succession. So, on your C5, it is helpful to use the old chain to pull the new one through, but don't worry about it if you forget, or if the old chain slips from the engine, or if you want to try to clean out the drive sprocket area before the new installation.