Okay, all kidding aside... I work in orthopedics primarily. I'm an anesthesiologist and work at an orthopedic specialty hospital. Although not a surgeon, I am probably capable of weighing in on this professionally...
Sounds like you've had shoulder surgery or recent injury. Without knowing the specifics, I would say that after either of those things; especially since you've been warned about lifting more than 5 lbs; I would refrain from range practice until released from light duty.
As others have mentioned, simple lifting is a fairly static activity. The imposed limit of 5 pounds is a fairly strict, suggesting that whatever was done to you (or you did to yourself) requires essentially no activity except that required of daily living (dressing, bathing, eating, etc.). Shooting is dynamic, and will place much more stress on your shoulder girdle than the simple weight of the gun.
Unless you want to end up visiting someone like me and my orthopedic colleagues to have that shoulder (my guess) repaired or replaced, be good to yourself. Do yourself a favor and borrow a SIRT pistol and/or do some dryfire drills if you really must.