The fun of watching the new play, Five Presidents in its east coast premiere at Bay Street Theater in Sag Harbor, is knowing the history moving forward from the momentous day, April 27, 1994 when the most exclusive club in the world, consisting of living presidents, comes together in a suite preparing for the funeral of one of their own, Richard Nixon. Under Mark Clements’ fine direction, first Gerald Ford (John Bolger) who is on the wagon but circles the bar like a vulture, then Jimmy Carter (Martin L’Herault) who gets a tall pour of scotch from his predecessor, then a slicked wigged Ronald Reagan (Steve Sheridan), George Herbert Walker Bush (Mark Jacoby) and “the new guy,” Bill Clinton (Brit Whittle), arrive one by one swapping stories about women they have nailed, the conflicts of going to war and sending young men and women to die, the economy, a rehash of everything you know about their presidencies meshed with their individual personalities and leavened by liquor. As these were the years before the name Monica Lewinsky entered the public consciousness, the name Gennifer Flowers is a reminder of that president’s pre-election dalliance. A Reagan verging on his famed senescence speaks inappropriately of a particular intimate act with Marilyn Monroe.