At least one week, however you can wrap them in foil and freeze them and have a fresh potato when you want one.
How Long Will Cooked Sweet Potatoes Wrapped In Tin-foil Keep In The Fridge For?
Hopefully longer than 4 days as I am eating one while typing this that I've stored for that amount of time.
The problem is that they can get all dry on you. I eat them within three days after cooking them.