Mountains would be a good option, doubly so if you're all able to do a little bit of hiking. Shenandoah NP is not a bad suggestion for that.
Knoebels in Elysburg, PA is a fun amusement park option. They have a great selection of rides and activities that are suitable for the younger side, and the free admission/pay per ride option works out nicely for groups where not everyone wants to spend all day being mechanically thrown to and fro. I'd think a week might be a bit much there.
While it's somewhat further away, Letchworth State Park in New York is fantastic, especially if you like some hiking. Many of the trails (or at least segments of them) would be well within the comfortable range of a five year old.