When I first started exercising, I was completely out of breath. I couldn't do anything for more than 5 mins(seriously). I find that as you progress into doing Physical Activity, you'll often succeed at sticking with it.
Take me for instance, as I progressed into Physical Activity, I started to do something I'd love to do, which is Walking. Anything from Walking to Swimming to Gardening is exercise. And chances are, when it's something you like to do, you'll stick with it in the long run.