Well you aren't getting in shape by sleeping. Yes sleep is crucial to a good fitness routine but sleep is not making you more fit. Also 5-6 hours isn't terrible if it is just one night.
If you have 4 workouts you do a week and you will move this workout to another day I say do that.
If you will simply skip the workout, I wouldn't. Since you are more apt to injure yourself while being tired, I would adjust my workout not skip it. It also depends on where you are with your routine. If you are concerned about strength, just go in and get the weight work done with a lot less reps per set than usual. If strength isn't a concern then do your same workout with less weight, faster.
Cardio... No reason to skip it. I would first make sure it is done after lifting. Second, I might lay off the treadmill or running. You are more apt to pull something being tired or distracted. So try biking, elliptical, stair-stepper - things that won't stretch your legs/core as much.
You will sleep tonight much better knowing that you reached your workout goals even when a little tired.