I started medical school at age 46, graduated at age 50 and now finished General Surgery residency (6 years) + vascular surgery fellowship. Can it be done? Yes, because I did it with average intelligence (IQ = 100) and uGPA of 3.9 with double major of Chemistry and Biology minors in math/physics. Yes, I had some community college credits and a very sound baccalaureate degree from the University of Virginia (Go Hoos!). I did residency at UVa after medical school and I got into every medical school that I applied to back in the dark ages of the 1990s.
My MCAT score was very competitive on one take, previous health care experience and a graduate degree (Ph.D) with significant research [molecular modeling and electron spin resonance/mass spectroscopy (TOF-MALDI)]. I didn't set out to become a physician/surgeon but was always a scientist (biochemist) and enjoyed what I did.
Now, I have a growing academic practice, an up and coming research lab and in a tenured position at a great university. I work 16+ hour days and work with a group of 7 surgeons of which I am the oldest and the only woman. Would I do anything differently? No, I am in great physical condition and love my demanding career. My guess is that my physiological age is far younger than my chronological age.
Am I heading for burnout? Not likely as that word isn't in my vocabulary nor is the word "tired". I am living my dream and enjoying the hard work. Retirement isn't in my future either. I am not superhuman (far from it) but I do have certain innate abilities/gifts that have made me quite suited to surgery/medicine not the least of which are good instincts, an ability to learn quickly, an ability to function well on less than 4 hours sleep and good hands.
What you have to ask yourself realistically is are you mentally and physically able to do this job? I have medical students who are age 21-24 who are not going to be able to do this job and medical students who are over 40 who will thrive in medicine (one of which is a natural surgeon). I will be the first to tell you that everyone who "dreams of being a physician" isn't even close to being able to do this but age isn't the determining factor.