Cover the tapioca with water and soak all night. Then boil it till tender. Make a custard of the five yolks, sugar and milk. Drain the tapioca. Put it into a large basin, adding a very little salt. Pour the custard over it and beat well together, adding the vanilla. Whip the whites to a firm froth. Stir them lightly in. Butter a pudding-dish and pour in the mixture. Set it in a pan of boiling water in a very moderate oven. Cover it with a dish. Bake until the custard becomes thick and a little set (it must not be as firm as a baked custard). Brown with a salamander or set in a hot oven for a few minutes.