The quick answer is yes. I waved goodbye to 46 years ago, and I'm not only doing cardio, but I'm also doing stregnth exercises, building muscle mass, stage combat, and more.
The limiter isn't your age necessarily, it's the state your body is in. If you aren't active right now, start with easier cardio workouts. If you're in reasonably good shape, pick a workout (or program) and run with it. I usually go with programs and try to complete the day's workout at level 3. Sometimes I can, sometimes I have to stop at level one. Every day and every workout is different and listen to your body.