You can participate in racing at any age. But as far as racing on the world stage, at the top level, you're starting out 15-20 years too late. That's assuming that you have the natural talent to be a professional cyclist, and the right genetic make-up.
Depending on where you live, there are a few hoops to jump through, too. In the US, for example, you need a USAC license, and then work your way up from the bottom, called cat 5, which will require actually winning some races along the way to advance beyond cat 4. I'm sure that other countries' federations have similar requirements.