Find yourself a good group to ride/train with. Your first couple of races should be focused primarily on staying with the pack. A good group can teach you a good race mentality, and some strategy.

If you're in good shape, you're in good shape. Age doesn't really matter at that point. That's why you start at Cat 5.

And, yes, I've known people that have gotten into racing in their late 30's and were strong enough to compete well.