The movie never gives us Highbottom's direct age. However, the book tells us he came up with the idea for the Hunger Games at the end of college alongside Snow's father.
His concept was later used to create The Hunger Games. The games didn't start until Coriolanus was 8. If the pair were around 22 at the end of their university days and young Snow was born soon after they graduated, give or take a year or two, Highbottom is likely at least 40.
Peter Dinklage, who plays the troubled creator, is 54.