I think that depends on the groups that exist near you.

I know someone who was in a similar situation (divorced around 50), and she found a local hiking group of divorced people who wanted exactly what you're looking for. So maybe ask on a local group on some social networks?

Hiking specifically is great because it's an activity that both kinda forces people to talk, and also supplies a default topic for conversation (It's also free, healthy and doesn't require special skills). If you're not into hiking, maybe a book club? Volunteering groups, like other people suggested, also fits that bill. Point is, don't just look for [an activity] with people your age, think about how much that activity is conductive for making friends. Something with 10% people your age, but that encourages talking with each other, might be better than something with 90% people your age where the group listens to a teacher together and then everybody does their own thing separately.

Also, It might actually get easier to find new people in a few years. Some people wait for their kids to grow up/move out before divorcing, which creates a spike of single people at that age.