Is there a botanist in the house?

After most of a lifetime living in the north, I knew the names of just about every fruit and wildflower in the region. Since I've been in the south, there's still a lot of flora and fauna I can't identify. This fruit is one of them.

It's about the size of a large golfball. It's pretty hard but you can squish it easily by stepping on it, and it's full of those seeds that look like very plump pumpkin seeds. It just seems to be the seeds and some stringy flesh inside and it's vaguely fuzzy but not at all furry. It grows on a shrubby tree in my neighbor's yard or maybe it's just a really large bush. Any idea what it is?



I'll admit I didn't try to ID it at all. If I google it, I get so easily sidetracked that I'll end up lost on some site discussing the finer points of chickle or something. So I'm trying to tap the group knowledge first.