Yes, define old....
I've had a few injuries, nothing major and it didn't take me a long time to heal. You just can't be afraid of getting hurt. I mean, I am a cautious rider, but i expect that as in any sport, there will be injuries. I have crashed pretty hard, once going down a 20% grade hill. Other than road rash and soreness (not to mention embarrassment), I was fine. I've learned to treat these things on my own. One of my first cycling injuries was when I was still riding the old Voodoo mtb on the road. I was going up a hill, when my son came down the hill on his cross bike, heading for the woods. He asked me to hand him my water bottle for a drink and I did. But when he went to give it back to me, I freaked and went down. About 5 days later I woke up with a huge lump on my knee. I did go to an ortho doc for that, but it turned out to be nothing but a hematoma. In other words, a huge bruise. I stretched, iced and took Advil and was riding again in 2 weeks.
I am going to be 55 in 2 weeks and while that might be old to some, it's not to me.