"Mom, can I watch Death Note?"
"No, too violent for you right now!"
My neighbour Totoro is a great anime if you want to introduce your little ones to anime. Your five year old may not be able to watch Death Note yet, but he/she can enjoy MNT for sure. It's very cute, and falls under the Kodomo demographic. Kodomo means manga/anime for very young children, usually around kindergarten age. For viewers in the UK that's reception. Outstanding art, story and characters.
Story:
Ten year old Satsuki and four year old Mei move house to the countryside. Once inside the house, the children explore. They find black Soot Spiders in the attic. An old lady tells them the soot spiders are nothing to be afraid of. The following day Satsuki and Mei go into the forest and find animals living there that can only be seen by kids. Totoro, a large, sleepy rabbit-like creature introduces Satsuki and Mei to his perfect world.
By Otaku55