I agree with what everyone said here, I would just want to add that you want to be prepared to supervise this dog at ALL TIMES. If I turn my back, even for a second, Tosca will often be getting into something she shouldn't. We've learned over the last two years what she will go for most (remotes, DVD's, and any kind of paper) so now those things are not w/in her reach and it is not so bad.
I would say the only other BIG stress is the factor of running away and eating things the dog shouldn't. Tosca will not just chew, but actually eat, pen caps, bottle caps, batteries, remote piece, medicine, etc. Not that mine has actually eaten these things, but would in a heartbeat given the chance. She did eat an entire child's sock once, but luckily threw it up before any real damage occured. The running away thing can be very difficult. Once your family has learned to adapt to it, it should not be hard, but it might not be easy to get a five year old to understand the need to make sure the dog is nowhere near the door when it opens. It is also very stressful when you have guests over or need to take the dog places. At least in my situation, they just don't understand that you cannot leave doors open, or let them close gradually on the way out, or your basenji will be GONE. I've had several times where we've had people stay over, and Tosca will be sleeping with me in the bedroom, and I wake up, let her out the door, and for whatever reason, someone will be going to their car or whatever, leave the door open, and out she goes. Not a pleasant way to wake up! I've learned from this now, and keep her on a leash or hold her when staying over somewhere/or when guests come over.
However, if you can get by the need to constantly supervise your dog, they really are wonderful dogs to have. From reading posts on here, it sounds like the dogs can be very different, but mine is the sweetest, most affectionate dog I've ever seen. She sleeps great, never has to be let out in the middle of the night, is crate trained (before we got her, thankfully), never needs to be bathed, and is wonderful with children. She is absolutely hilarious, and she makes my husband and I laugh all of the time. Like I said, if you can deal with the large amount of effort/supervision this dog needs, I think you'd be really happy with a basenji…good luck!