5 card stud is one of those games that puzzles people. Whenever you mention it people say something like "you mean 7-Card Stud?" or "how's that different than Draw Poker?" But 5-Card Stud is a game unto itself although you'll seldom see it played these days. There are a few good reasons for that, but let's cover the basics first.
Betting Limits, Buy-In, Bankroll, The Ante, and the Deal are all pretty much the same as 7-Stud and I refer you there for these details. Keep in mind that because 5 Stud is seldom played in the casinos these rules often vary. The truth is that 5 Stud is mostly played as a social game these days, so the rules flex according to the player's tastes.
A round opens with the dealer giving each player two cards. Traditionally the first is a pocket (hidden) card and the second is open (face up). There are variations on this and we'll see why shortly.
Now it's time for the first bets. Low card opening is standard but it's not uncommon for high card to open. The game progresses the same either way. The betting round circles the table and it's on to Third Street.
The third card is dealt to each player as an open card. Betting typically follows 7-Card Stud's Third Street play (Low Limit bets).
Another open card, typically played per 7 Stud's Fifth and Sixth Street (High Limit bets).
The final card, usually also an open card. Betting as per 7 Stud's Seventh Street(High Limit bets).
I've also seen games where Fifth Street was dealt as a pocket card.
The Trouble with 5 Card Stud
There's a real problem with traditional 5 Card Stud. With only one pocket card there's not much doubt as to what a player is holding. Furthermore, since there are only 5 cards per player and no discards, most hands are going to be pretty low, mostly pairs and high cards. At least in Draw Poker the player gets a chance to improve their hand by drawing new cards. Not so in 5 Stud: you're stuck with what you get and the other players can see most of that.
The end result? Players with even basic play experience will read the cards fast and early. They'll either drop or be going for the pot and it's tough to drag anyone but a novice along for the latter streets. Bottom line is it's a slow game for anything but social events and "friendly" play. This is where the variations come in. The more interesting 5 Stud games I've played are those where there are two pocket cards. Sometimes it's first and last card, sometimes the two opening cards with the player on the dealer's left opening the bets.
In the end these variations are simply attempts to add a little suspense. The hands are still going to be low. And the extra pocket card just allows for a little more bluffing and the possibility of chubbier pots. The fact that even these variations only appear in social games tells the same story as before: 5 Card Stud has left the building.