Not that rational reasons should be given to shoot this idea down, but you do realize 5 minutes is about the average time of a drive, so you could lose a top player on maybe a weak or questionable call for a full drive, maybe 2 or 3 if it's a 10 minute call? I know it's the offseason, but let's get back to the reality of what actually might occur.
Example - Hughes goes to sack the QB ,gets a piece of his helmet, out for 5 minutes, chases RB out of bounds, gets a close call on late hit out of bounds, now we lose him for 10 more minutes. Defense on the field around 30 a game max - he's gone for 15 right now.