Having had a chance to think about this, I'd recommend a visit to Hakone using the Hakone free pass.
You'll have the opportunity to cover a lot of ground and see lots of the landscape and because you use a whole variety of transportation - rail, cable cars, ropeways, boats and only at the end a bus, you don't have to cover a lot of distance on foot, which I know will quickly get tiring for a 5 year old, and for both of you in August. Although the area in itself should give you a bit of a respite compared to the heat sink that is Tokyo.
More info here
http://www.odakyu.jp/english/freepass/hakone_01.html
If you decide to visit the Hakone Open air Sculpture park there are quite a few areas and exhibits which a child can enjoy and appreciate, the most notable being this one:
http://www.thejealouscurator.com/blo...iuchi-macadam/
I have this area in mind for a visit when my soon to be three year old reaches your child's age.
Nearly forgot!
Please take care to ensure that your daughter has shoes that she can slip on and off easily as a great many of the play areas that you will come across (sometimes randomly) will be no shoe zones. If wearing sandals, you should also always have some spare socks to hand, preferably with a bit of a non slip tread incorporated into them. And this goes for you too. You may need to rush into any of those no shoe zones and big adult bare feet (particularly in the summer) won't be warmly welcomed.