Four Cards Tell All

A magician and her assistant perform with an ordinary $52$-card deck. A spectator picks any five cards and hands them to the assistant. The assistant secretly examines them, keeps one hidden, and passes the remaining four to the magician one at a time in an order of the assistant's choosing. From nothing but the identities and sequence of those four cards, the magician names the hidden card — correctly, every single time. Design a scheme that makes this trick infallible, and explain why it works.