Nowadays, with the advance of computer, and the ease of travel, more and more young kids pick up the wood very early and make great progress at super-fast speed. The GM record has been lowered from high teens to low teens. The current record is 12 years old.
The best age I suggest is still 6-8. 5 is a little bit young, but can possibily work. 4 is too young for any chess school. Above 8 is a little late and require too much efforts to overcome the late-starter disadvantage.
Based on the observation in last 10 years, the average student can reach expert level (2000) after 100-150 tournaments. If your child play 2-3 tournaments a month, that will take 3-5 years. If s/he wants to be a master (2200), then add another one to two years. Add half to one year before her/his first rated tournament. Overall it might take about 8 years for a child to become a master after s/he made her/his first move. This means s/he would become a high school student and would be very busy with her/his academics.
So, going backward, it's better to start early, and start slowly so s/he could have a solid foundation. We can have enough time to observe and decide if s/he has potential.