As long as you are in relatively good health, and somewhat fit, I don't think there is an upper "too old" age limit. My advice to any older person thinking about either resuming or starting backpacking would be to first get a checkup from your physician. If you get a "go ahead" from your MD then start out with day-hiking. Carry a pack containing your "ten", or "fourteen" essentials and gradually add weight to your pack as you become fitter. Gradually increase both weight and distance hiked. If you are overweight, loosing weight is the cheapest way to lighten the load on your feet and it helps your back as well.
Start to assemble a light weight kit and plan your first overnight. There are gear lists posted on the home page of this site to give you some guidance. Your first overnight should not be particularly ambitious; early efforts should be "dress rehearsals" for future, more ambitious, ventures.
As OM noted, there are several people on this forum who are in their 70's and still on the trails. I'm one of them: So is she. And, on a recent five day trip in the Sierra, I met a guy on top of Mono Pass (12,000')who was 82 and returning from a four day trip.
I have the ambition of section-hiking the entire Pacific Crest Trail while I am in my 70's. So far, I have hiked the section between Kennedy Meadows and Tuolumne Meadows and the northern half of the Washington section. I doubt that I'll make the entire trail in the five years before I turn 80 but that is OK. To quote Robert Browning, "Ah, but a man's reach should exceed his grasp -- or what's a heaven for?"
I, too, have periodically suffered lower back problems. In my experience, the walking is good for one's back but YMMV.
May I walk in beauty.