This article is from the Piano General Topics FAQ, by Isako Hoshino firstname.lastname@example.org with numerous contributions by others.
The answer to this question is an emphatic "No! One is never
too old to start!" All you need is love of music, love of
the piano, interest, perseverance and enthusiasm!! (well...
and an access to a keyboard of some sort) As an "older"
student, you actually may have the advantage of quicker
understanding of the concepts, and better motivation since
you know why you want to play. Also since you are the one
initiating the learning process, you have a better chance of
succeeding in your goals of becoming a piano player (some
kids just start playing because their "parents told them so,"
and that won't get them too far in the long run).
Piano playing does wonderful things to the human mind and
body. There have been reports where an 80 year old person
started to learn to play the piano, and in so doing, improved
his motor skills, mental agility and overall well-being, and
went ahead and became an excellent player! So don't let
those 5-year-old seemingly prodigious kids discourage you!
Just go ahead and start learning!