Never too old to learn! I am about your age (born on 1984), and I have just self learned breaststroke (by observing other swimmers). Come on! You will definitely enjoy swimming. 25 is a golden age to learn!
Definitely not too old! And even if it takes a while, it is a good idea. Over a third of American adults can't swim more than the length of a standard pool, according to a 1994 CDC survey, and another study reported over half of 12-18-year-olds can't swim either.
And you don't want to be in the position of six teenagers who drowned in a Louisiana river, trying to save a friend who accidentally stepped out of a shallow wading area, or the nonswimming adults who stood on land, unable to help.
I am an avid swimmer myself, and I have encouraged both my daughters to swim at an early age. My mother-in-law, on the other hand, has fear of even standing in water that's above her waist. Of course she could start to learn to swim, but at an older age I think there are three inhibiting factors: (1) Fear - if you have a fear of water, you need to learn to overcome that, perhaps even by means outside of swimming lessons, (2) Desire - for young kids, water is about playtime so swimming comes naturally, whereas for an adult, you may have to discipline yourself to get in the water regularly, and (3) Strength & Weight - as you get older (and bigger) you have to focus more on movements to keep you afloat that may tire you out until you perfect them, so you may need to consider physical conditioning outside of the pool as well, such as arm exercises. Overall, I must say that as I've gotten older, I have come to love swimming even more than when I was younger. To me, swimming is cathartic and refreshing, submerging you into almost another world, apart from the ordinary. And swimming really comes to life if you can take it to the open water in a lake or safe ocean area.