In your sixties
Definition 1 of 1
Pro Tip 1/3Age Precision
This phrase doesn't specify an exact age, just that someone is in their sixtieth decade. 
My neighbor is in his sixties, always forgets his exact age!
Pro Tip 2/3Conversational Tone
'In your sixties' is casual, often used in informal talk about age without requiring exact numbers. 
At the reunion, I noticed that many of my classmates are now in their sixties.
Pro Tip 3/3Cultural Perception
Culturally, this phrase can imply approaching retirement or having grown-up children. 
My parents are in their sixties, so they're thinking about selling the house and traveling.