Popcorn has always been irritating to my digestive system but usually caused the opposite of constipation (sorry). Now that I have diverticular disease, I avoid it like the plague. I'm sure you don't have to avoid it, but I wouldn't recommend that anyone eat 5 cups every day, especially if it's making you uncomfortable!
If it's really bad, I would recommend calling your doctor. Otherwise, lay off the popcorn for a couple of days until the rest of it leaves your system, then add it back in slowly and see if your symptoms return. Food sensitivity is often a matter of trial and error.