Bad back

Let your back heal before you go back at it. Don't sit (that can make it worse) but don't go back to doing very strenuous things until you're better. Walking is fine but let your back tell you when to stop.

And then when you're better, check your form for the exercise you're doing. Most back injuries (ETA and knee injuries, too) are a result of poor form. Have someone look at the DVD (I'm not familiar with the one you're watching, but hopefully they demonstrate and exercise before they require you to do it) and have that person watch do do your the exercise to see if you're doing something wrong - maybe flattening the natural lumbar curve of your spine, or hunching over or something of that nature. If you don't have another person to do this, try looking in a mirror while you do the work and see if you are keeping correct posture.

53 is not too old to start exercising - no age is! It might be that the DVD you've chosen is too intense for your current ability and you might have to modify some of the work or do a less intense one to get into better shape first. If you have not been active for years or if you are very overweight, that might be the case. Again, I am not familiar with the DVD you're talking about but some (I know the 30 day shred does, for example) have modifications for some work built right into the video so you can take an easier option while you work up to the harder one.

I know more than I want to about back injuries as I have an L3-S1 lumbar scoliosis with bulging discs and impinged nerves (now apparently on both sides, yuck) that is eventually going to require major, lifechanging surgery, but even I can manage a short run and weightlifting with proper form and understanding my limitations. I see no reason that anybody at any age can't exercise, and more likely than not your injury is muscular instead of spinal.

If it doesn't get better, if the pain moves into your hip and leg, if it gets radically worse, see a doctor. If you feel you need to pee or poop but cannot, OR in the alternative lose control of your bladder or bowels, see a doctor IMMEDIATELY AND DON'T WAIT. Other than that, rest (but not too much), heat at first and then ice, and when you're better make sure you're keeping your lumbar spine's natural curve and doing your exercise with proper form, and you'll be all good.