If you're only 5yrds away from somebody you don;t even really have to aim. A coworker and I have started doing a pistol drill when we go shooting. You staple 3 standard paper plates to post. Starting at a distance of 10 yards you get 10 seconds to put 10 rounds into the first plate. Then at a distance of 7 yards you get 5 seconds to put 10 rounds into the next plate. Lastly at a distance of 5 yards you get 2.5 seconds to put 10 rounds into the last paper plate. My first attempt I scored 6/10, 8/10 and 10/10 respectively. The last time I did it I managed 9/10, 9/10, and 10/10.
I will be the first one to admit that I suck with a pistol, I have no training or back ground with them at all and have only owned one since April of this year. My background with the Army is fully automatic weapons, primarily the M249 and M2. I've spent more time in my career shooting an M249 than the M16.
The point I'm making is that even the first time attempting this drill, and with me and admittedly terrible shot with a pistol (though improving) I could still put all 10 shots into the paper plate at 5 yards in less than 2.5 seconds. While 15 feet isn't by any means a great distance, it seems the majority of all LEO shooting deaths occur within 10ft. I would think that with a small, easily concealed handgun like the LCP .380 that as long as you can accurately shoot it within 10 yards you're doing good. While that paper plate isn't a small target, neither is the chest cavity of a human being. CCW weapons aren't intended for long range, extended gun fights. Thats what full size handguns, and preferabbly rifles are for.