Asian elephants can typically live into their mid-50s. However, a few have made it into their 80s. Lin Wang, an Asian elephant at Taipei Zoo in Taiwan, lived to be 86. At the time of his death in 2003, he held the Guinness World Record for being the oldest elephant in captivity.
Dakshayani, an elephant at the Chengalloor Mahadeva Temple in Kerala, India also had a long life. Given the nickname "Gaja Muthassi" (meaning "elephant granny"), she died in February at 88 years of age.
In the US, there are several Asian elephants in their 70s: Shirley, who lives at Tennessee's Elephant Sanctuary, is 70 years old, while Ambika at the National Zoo in Washington, DC is 71. It's worth noting, though, that these ages are often estimated.