Imagine you and four friends deal out a hand of a game of poker, and look at your hands. Each person is dealt 5 cards, and the remaining 27 cards are still in the deck. Unfortunately, the game is interrupted before it has a chance to start. You decide to memorize your hands, and play the hand tomorrow. The next day, you want everyone to somehow get the same 5 cards they had yesterday out of a shuffled deck, without gaining any information about what cards the other players have. All players are assumed to be honest, and will not cheat in any way.
This puzzle is my own design. I will eventually post the solution in the comments, but if you solve it before then, show off and post your own solution.