I have been teaching Karate for 30 years and in that time have taught beginners from 5 years to 62 years (Jim P., who was a member of the first ever Gym/Health Club in Perth, suffered several strokes but said Karate kept him alive). Presently we only take students from 16 years and up, as we are holding adults only classes. I find many people have done a little of some Martial Arts in earlier years and are quite surprised how quickly it all comes back to them.
With advanced age, everyone may find one or another technique harder or impossible to perform. Let this not deter you. Karate is a martial art, and as such it is self-defense system, not a display of superhuman ability and athleticity. There is no shame in not being able to pull off a triple spinning flip kick. Chances are that in a real situation a simple front kick would have been the better option anyway.
All the benefits of Karate in terms of self defense skills and improved health still apply, regardless at which age you start. With increased maturity you will also be in a better situation to judge what exactly YOU want to gain from Karate training, and you will be able to focus on that in our classes - this way you'll gain maximum enjoyment and benefit from Karate training, regardless of your age.