We have just signed up too. I totally recommend Ham House, just past Richmond.
There is an activity trail inside the house that your 5 year old would probably like (my 6 year old did), which gave us a bit of free reign to admire the historic paintings and furniture. The gardens are extensive and beautiful and they let you borrow (for free) activity sets to play with in the gardens, plus there were other things going on when we were there, like "build a den". Lots of families enjoying the atmosphere. The cafe is very good too for lunch or snacks. Final thumbs up is that it is right on the Thames with a path going alongside.
We are definitely going to get our money's worth from the membership because we are doing a few UK holidays this year with NT properties nearby.