Nomad
Master Black Belt
I don't take students under the age of ten, regardless of medical conditions. You have to look at the big picture and ask what the school is teaching. If they are teaching kicks and playing games a lot, it would be a good place for a young child. If the school is teaching wrist locks, arm breaks, and takedowns (like mine), do you really want a five year old learning that?
AoG
I have to disagree on this one. Classes should be kept age-appropriate, but can definitely be way more than babysitting. This is where the foundation can be laid, and if done right, will mean excellent technique as the child matures and an abiding love for the martial arts.
Our school teaches from 6 years old up (they also have a program for 4-6 year olds, but that one is more a primer... teaches listening skills, etc. through storytelling and role-playing with the kids). The classes for the 6 year olds have much of the same course material as those for the 12 year olds and the 37 year olds (like me), but the emphasis, approach, and manner of teaching differs from class to class. We have several people who have been in the program since they were 4-6 years old, and they are great technicians who make those of us who started significantly later in life look stiff and graceless by comparison.
It is also easier on the philosophy side (if your school is into that sort of thing). Starting early on some of the simpler concepts can be beneficial, as kids don't have nearly as many preconceived notions and other mental "baggage" hanging around as adults do. It can also help refine the child's own moral compass simply by talking about whether different things are right or wrong, etc.
My two daughters and I all train at the same club, which makes it easier to discuss different ideas. I can also help them through technique problems when they arise. In return, they're a great motivator for me to stay active in the program. Working out well so far at least...