You're right -- Safety First.
Age 5 is fine. For starters, get hold of the NRA's Eddie Eagle gun safety program. This is an excellent introduction for kids who are going to be around guns, but are not yet ready to responsibly handle them.
We got the videotape when our daughter was about 7, when the household acquired a .22 rifle. But the Eddie Eagle program doesn't require that you have a gun around; it's good safety training in case your daughter encounters one anywhere. You've read the stories about kids under 8 accidentally shooting themselves or somebody else. There's just no need for that kind of tragedy.
Once she's got the basic idea that guns are something to respect, and you determine that she's developing a good sense of responsibility, a small firearm (like the BB gun lp boonie suggests, might indeed be appropriate). Let her level of interest guide you -- some kids take to firearms, others don't. Mainly, I believe she should be trained in safety first, then given the opportunity to find out what she thinks about shooting. My daughter knew generally about gun safety for a while before she actually fired a gun, and that worked out well.
If your daughter shows interest and sense of responsibility, I don't think 5 is too young. It happens my daughter (and I when I first shot) were up around 12, but I wouldn't necessarily wait that long, especially if she's going to be around guns in the interim.
Please note -- my FRiend MikeJ was invaluable as a teacher when my daughter became active, and so I've pinged him on this. He's got a lot of experience as a teacher, and I'd go by what he says.
I've got nothing to add - you've covered it very nicely.