Grease and flour a 8 x 12 inch pan. Preheat the oven to 350 degrees F (175 degrees C).
Separate 5 eggs, and beat the egg whites in a large mixing bowl. Add 1 cup sugar slowly to the egg whites, beating constantly. Add the yolks one by one, beating well after each addition. Stir in the 1 teaspoon vanilla. Sift the flour, and stir it into the egg mixture. Pour the batter into the prepared pan. Bake the cake for 20 minutes, or until done. Cool.
Blend the sweetened condensed milk, evaporated milk, milk, and 1 tablespoon vanilla. Pour this syrup over the cooled cake.
To make Meringue Frosting: Beat 3 egg whites to soft peaks. Gradually add 1 cup sugar, and beat until stiff peaks form. Stir in 1 teaspoon vanilla. Frost the cake.