76 in the first Hunger Games film, according to Donald Sutherland
In 2012, around the time that the first film was released, Donald Sutherland was quoted in an interview as saying:
And those scenes aren't in the book. He wrote them and Suzanne Collins loved them. But it so perfectly described what someone — an administrator, a bureaucrat, not even a leader — that Coriolanus Snow is and that he has to do. How do you keep that underclass in control? You offer them a little bit of hope. He thinks that Wes Bentley's character would probably take over his position. He [President Snow] is 76 years old, he was two years old when the Hunger Games started. And he's looking for a successor. And he tests Wes' character. "You've allowed this girl, this underdog. Do you like underdogs? You've allowed her to take some kind of position of power"... When you fail, you die...
The uncredited claims about his age in the Wikia and on various other sites almost certainly originate in this interview.