I started at 49 and it's the best thing I have ever done for myself for many reasons: I benefit physically, mentally, and spiritually. I have something else in common with my daughter. It's fun striving together.
About the physical part. The key is to push yourself yet pace yourself; don't try to keep up with the higher belts. You gain stamina and strength over time. I have more stamina than some of the teen boys/girls starting out. They can't keep up with me during one-on-one kicking. Last year, after only 5 months of training, I entered a competition and sparred against women younger than myself. In fact, one was 24. I placed second. (Boy, was I surprised, lol.) At 50 you may be slower but you can be more wily
Of course, if you want to, you can gain speed by practicing.
Learning wrist grips, forms, and one-step sparring combinations can be overwhelming. But that's great for the mind, builds new pathways in the brain.
Not enough can be said about weight-bearing exercise for keeping your bones strong. Not enough can be said regards intense exercise for lowering LDL cholesterol and raising HDL cholesterol. Not enough can be said about losing dangerous intraabdominal bodyfat.
I plan to be doing this forever.