The tkd in my user name stands for Tae Kwon Do. I have a 2nd degree black belt, and was the senior instructor at a local school for about 3 years.
5 years old can be on the young side to do martial arts. We did take children at 4, but my own children didn't start until 6 and 7 and they were still pretty fidgety. If your child can focus on an activity for 20 minutes independently, they are probably mature enough, since no single activity would be longer than that. You will also find that in most schools, the students are totally on their own. Sometimes the parents can watch, but often times, the class is on the other side of a wall, and parents are out of sight.
Good schools will offer a variety of options for classes. They can be broken up many ways such as by age, by belt level, by the focus of the class, etc. I would strongly suggest either a kids class or a Little Ninja's type program. Little Ninjas usually are for the younger kids, and have some lower requirements. For instance, they might not do any sparring, or they might only have to do kicking combinations, or they might not need to learn the terminology. They also are more focused on activity, and the classes are usually shorter, with more teachers.
I think the most important thing in any martial arts school is finding one that has an appropriate level of respect for the discipline that you're teaching. Any martial art is NOT a game, but has real life consequences. In our school, any student who repeatedly used his skills outside of class was no longer a student. Our master also requires all his young students to bring him copies of their report cards. They got "stars" for all As, and stars if they had made improvements from their previous grades.
Try out a variety of schools. Most will offer the first lesson (usually in street clothes) for free, and they often have trial programs for a good price. We offered a 2 week program for $29 and a 6 week program for $99 which included the uniform. This provided 2 to 3 classes per week. I will also say that martial arts is not a one night a week activity. If you take less than 2 classes per week, you're not going to learn enough quickly enough. So be sure that the school you choose has enough flexibility to fit into your schedule.
Good luck!
Our teachers do not allow students to participate in tournaments that allow contact. Jr black belts (under 16) gets points for being within 1" of the target, but can be disqualified for actual contact. Lower belts have different distances - depending on their experience.
