It is impossible to keep a 5lb dog in a fence.
Well, that is, of course, simply not true. It is impossible to keep a five pound dog is some fences, to be sure. But I have literally hundreds of customers with 3, 4, 5 or 6 pound dogs, and they all stay in their fences just fine. My eight pound dog has never gotten out of the fence.

You stated that you weren't the right home for a small dog, however. I think you need to stick with that. If you do decide to get another dog, I think you need to get a larger dog.