Depending on the specific lines about 40 to 45 ft of a 3wt line will weigh about as much as 30ft of a 5 wt line. The 3 wt line will cast fine on a 5 wt rod as long as you have sufficient line out. Not much fun if casting in close all day unless you are just fishing using short line nymph/Euro/Czech techniques. Like others have mention I too have got to the water with the wrong reel/line for the rod I brought.
I cast 3 wt lines on 12 wt rods a couple times in demonstrations. It works but it's a chore.