Is it ever too late to get into music with the intention of making a career out of it? If so, when?

Mozart wrote his first symphony at the age of 8. Being ten years older, I can barely even play one single instrument properly. Now, while I know that you don't have to start out that early in order to be successful, I wonder, how much does it really matter to start out early? Can you become a good musician even if you first started to get an interest in performing at the age of 17? And since genre probably matters, I guess I should mention I'm thinking either contemporary clical or swing.