Nelson Mandela is THE example to bring up on the news shows, followed by Winston Churchill. Everybody's heard of Mandela and seen that rugby movie featuring him, Invictus. That should shut down anyone saying he's too old. "What if South Africa had thought Mandela was too old?" Point, set, match.
Maybe not a universally popular choice, but Deng Xiaoping rose to leadership of China at the age of 74 and held the post until he was 88, and in my opinion did as good a job as anyone could reasonably expect given the constraints of the situation.
Nelson Mandela, Charles de Gaulle, Konrad Adenauer, Winston Churchill, George Washington, Ben Franklin, Eamon de Valera (re-elected at 84, retired at 90 years old), and Golda Meir are the best examples. Michaelangelo and Moses, if you want to go there, are other great examples.
per Wikipedia, Gandhi was shot and killed by an assassin in 1948, at the age of 78, as he was about to give an address. He was working for Indian independence up 'til then, even having been jailed most recently between 1942 and 1944 (age 72-74).
Why does your friend care what his age is? If he's healthy and honest and for positions your friend likes what does it matter? Would he prefer a young tyrant?
Exactly. What possible rational basis is there for selecting a president based on age? Worried that he might die in office? If you trust him enough to be President, you trust him enough to pick a good vice president. Problem solved.