7-5-3 is pronounced shichi-go-san in Japanese and expresses the ages of the children the festival celebrates.These ages are considered important in a child's life. The festival is said to have started in the Heian period (794-1185). It is still very much celebrated today and it's main day of celebration is November 15th.
Since this day is not a national holiday, most families pay their shichi-go-san respects on the weekend just before or after then. Meiji Jingu Shrine in Tokyo is one of the best place to go if you want to see them all dressed up. By the way kids are fun to photograph!