My two cents:
1. There's no rush. Have him help when you clean your weapons after your next few range trips. Explain to him the parts, their function, how a safety works, etc. Let him do a bit of scrubbing. Understanding how the system works will deepen the foundation. Taking away a bit of the mystery won't take away the fun. Remember, though, that he's 5 and has the memory span of a goldfish; much of this will be lost on him. Repetition is the key.
2. Take him out and shoot some cans or a target taped to a cardboard box using one of those break barrel pellet guns. It's quieter, produces less recoil, the sights work the same and you get to watch cans fall over. Every little boy loves to watch cans fall over. Better, you can start shooting at closer ranges, so he'll improve faster. If it's just the two of you, it could be great education as well as bonding time. You can talk to him at length about the rules of safety or how crappy the Cubs are going to be again this year w/out constantly being drowned out by the guy sighting in his new 7mm Mag 3 lanes over. Also, it's safer for you and those around you; if your boy ADs using a pellet gun, there's only a slight chance of severe injury.
3. Move up to the range and a real firearm after you think that step 2 has brought him up to speed.
Enjoy it. You both will have great memories.
I'm right about the metric system 3/4 of the time.