Should I work out even though I am sleep deprived?

It's the afternoon, and I always have sleeping problems so I normally skip a day during the week of working out and make it up the next day. Like normally I would work out M T Th F. But sometimes I'll do M W Th F. I feel weak when I can't sleep so it sucks... I do stuff in the afternoon after workouts on Tuesdays so thats why I skip it. I can take naps on the rest of the days when I'm tired.