See V. I. Seroff, The Mighty Five (1948); M. O. Zetlin, The Five (tr. 1959).
Play begins with each player being dealt five cards, one at a time, all face down. The remaining deck is placed aside, often protected by placing a chip or other marker on it. Players pick up the cards and hold them in their hands, being careful to keep them concealed from the other players, then a round of betting occurs.
If more than one player remains after the first round, the "draw" phase begins. Each player specifies how many of his cards he wishes to replace, and discards them. The deck is retrieved, and each player is dealt in turn from the deck the same number of cards he discarded so that each player again has five cards.
A second "after the draw" betting round occurs beginning with the player to the dealer's left or else beginning with the player who opened the first round (the latter is common when antes are used instead of blinds). This is followed by a showdown if more than one player remains, in which the player with the best hand wins the pot.
Another common house rule is that the bottom card of the deck is never given as a replacement, to avoid the possibility of someone who might have seen it during the deal using that information. If the deck is depleted during the draw before all players have received their replacements, the last players can receive cards chosen randomly from among those discarded by previous players. For example, if the last player to draw wants three replacements but there are only two cards remaining in the deck, the dealer gives the player the one top card he can give, then shuffles together the bottom card of the deck, the burn card, and the earlier players' discards (but not the player's own discards), and finally deals two more replacements to the last player.
The sample deal is being played by four players as shown to the right with Alice dealing.
All four players ante $1. Alice deals five cards to each player and places the deck aside. Bob opens the betting round by betting $5. Carol folds, David calls, and Alice calls, closing the betting round. Bob now declares that he wishes to replace three of his cards, so he removes those three cards from his hand and discards them. Alice retrieves the deck, deals a burn card, then deals three cards directly to Bob, who puts them in his hand. David discards one card, and Alice deals one card to him from the deck. Alice now discards three of her own cards, and replaces them with three from the top of the deck (Note: in a player-dealt casino game there is often a rule that the dealer must discard before picking up the deck, but this is a home game so we won't worry about such details). Now a second betting round begins. Bob checks, David checks, Alice bets $10, Bob folds, David raises $16, and Alice calls, ending the second betting round. Alice shows a flush, and David shows two pair, so Alice takes the pot.