Adult triathlon's are fun, but kids tri's are a blast. Kids triathlon's usually allow kids from 5-15 yrs old. It gets more competitive for older kids, and more fun for the younger ones. Everyone supports finishers from the first to the last.
5-6yr old tri's are normally short distances approx 25 meter swim, 1 mile bike ride and 1/2 mile run. The swim is too sort to make much distance, and kids run at a similar speed at a young age. So the winners are usually the best at transitions and cycling. Most young kids have heavy dept store bikes, which are very slow. Using a BMX micro-mini ( 15 lbs ) will provide a huge time advantage. Additionally, you should have your child use the new generation of sock shoes. Kids can swim in them, then ride and run in the same shoes. It will really help with transition times.