I’m going to give you an answer I really stand by – YES! You can learn how to play the guitar in your 50’s, 40’s, 60’s or at any age, really. Your age has nothing to do with learning the instrument; it’s your responsibilities and how crowded your brain is that make learning a new skill challenging.
Younger players have more free time if they choose to get serious about the guitar. Outside of school and perhaps a part-time job, their schedule should be free to pursue anything they choose. They can get better quicker because they have more time to dedicate to practice everyday. For adults, things are little more difficult, perhaps, but I have never met an adult whose fingers were too short or too long, or an adult who wasn’t able to grasp concepts of playing and so on. Adults don’t have as much disposable time as youngsters, but we do have experience in learning which is on our side. I actually strongly recommend learning any new skill throughout your life. If you set your expectations correctly and understand that picking up the guitar takes repeated committment for which you make time for – I say do it.