How Long Is It Safe To Keep Cooked Beans And Ham?

According to the experts, the general rule of thumb for keeping refiderated foods is four days. After that, they start to grow bacteria.

I will give you the same answer I gave to the blurter who asked how long homemade vegetable soup would keep in the fridge.  If your family is eating what you cook, this shouldn't be an issue.  ;-)  Seriously, though...just remember the nursery rhyme "...pease porridge in the pot...nine days old."  If the ham and beans ("pease" is the old-fashioned word for what we call "legumes" now) are still in the fridge after seven days, make sure you serve it for lunch or supper that night.  I've worked in many restaurants and other commercial kitchens over the years.  One owner had an expression:  "It's still good.....but sell it today."
And if your family isn't eating your beans and ham dish, maybe you need a new recipe for beans and ham.  ;-)