It depends on the season. In early May, I could do three sets of twenty push-ups flat out. By the end of May I had a lung infection which has not fully healed. Today I did push-ups for the first time in five months, since I became ill. I could do about 3 flat out, and 17 more on my knees. I have a long ways to go until I get back to where I was last spring!
I am 55 years old, so it is never too late to do them!