I used to play a game called Seven Card Sweat.
The game was very simple and it was purely for fun / to gamble. It is also very similar to what you are describing.
Each player is dealt seven cards face-down. The first player reveals their first card and stops. The second player reveals cards until they have a five-or-less card hand that beats the other players. This continues until all players have revealed all of their cards, and the player with the best five card hand at the end wins all of the money.
The turn taking is purely for entertainment e.g. the sweat aspect. There is no strategy.
For example two players:
Each get dealt seven cards face-down.
Player A: K♠ ---
Player B: 2⋄ 3♥ A♠ ---
Player A: K♠ 8⋄ 4♥ 9♣ 4⋄ ---
Pair of Fours
Player B: 2⋄ 3♥ A♠ A⋄ ---
Pair of Aces
Player A: K♠ 8⋄ 4♥ 9♣ 4⋄ K♣ ---
Two Pair; Kings and Fours
Player B: 2⋄ 3♥ A♠ A⋄ 4♣ 7♠ 5♠ ---
Straight; Ace through Five
Player A: K♠ 8⋄ 4♥ 9♣ 4⋄ K♣ K♥ ---
Full House; Kings full of Fours
Player B: "Wow that's so sick. Take your money!"
It can be played with as many players as the deck allows, which is seven.