The requirements to getting a MLB championship ring are winning an MLB championship. There should not be a time limit for players being on the team.
The losing team of the championship game in the NFL, MLB AND NCAA do get a ring from the leauge. The NBA and NHL do not but some of the teams make rings with their own money for the players but the league itself does not pay or hand out rings.
There isn't a player with five, but there is one with six. The MLB player with six championship rings, and none of them coming with the Yankees is Eddie Collins. Collins won five championships with the Philadelphia A's and one with the White Sox.
Yogi Berra has won more World Series championships than any other individual player. He won 10 out of the 14 in which he played. Both numbers are records for individual players. If anyone has the most rings, it would be Yogi. Although Yogi also won 2 rings as Billy Martin's bench coach in '77 & '78, which technically gives him a total of 12 rings all together!
Yogi Berra with 13 Frankie Crosetti won 17 WS Rings with the New York Yankees(8 as a player 9 as a coach/the most title rings in all of team sports). 2nd is Red Auerbach of the Boston Celtics with 16 rings(9 as a coach and 7 in the front office).