You sure the bike's the right size for ya? Hand numbness can often be caused by improper fit. The unfortunate thing is that as a beginner to road cycling you don't really have a way of knowing what's suppoed to feel 'right'. A good idea might be to take yourself and the bike into a shop and get a nice bike fitting. They can shorten your stem, adjust heights, etc. to make riding a lot more enjoyable.

Anyway, good luck and have fun. The Trek 5000's one hell of a first bike! Congrats.