1. Combine 4 cups milk, rice and sugar in a saucepan. Bring to a boil, reduce heat and simmer until rice is tender, about 30 minutes.
2. Remove from heat and stir in salt and vanilla. Whisk egg yolks and about 1/2 cup of hot milk mixture. Whisk back into pan and add remaining 1 cup milk. Place over medium heat and cook until thickened, about 5 minutes. Let cool and chill at least 2 hours before serving.