Jimmy Carter's announcement that he's facing his own mortality made me think about the fact that right now, we have 5 living current and former U.S. presidents- Carter, Bush I, Clinton, Dubya, and Obama. Has there ever been a time when there were more than that?
I'm assuming it might have been in the 19th century, when there were a ton of one-term presidents.
I am aware that linking to Wikipedia is in large part deprecated, but since in this case the question is purely statistical with a concrete answer, take a look at the breakdown at Wikipedia's List of living Presidents of the United States. There have been at most 6 living Presidents at any one time since the establishment of the Union, the most recent being 2001-2004 when Jimmy Carter, Ronald Reagan, George H.W. Bush, George W. Bush, Bill Clinton, and Gerald Ford were all alive.