As a dad with kids of very similar ages, I can say your idea sounds like a wonderful experience for all. You have two challenges however at this stage of the game, the first being availability. You would need a wilderness permit for an overnight stay:
http://www.nps.gov/yose/planyourvisit/wildpermits.htm The advance reservations are now booked up for the entire summer on the popular trailheads and filling up quickly on many of the rest. (See the full trailheads report on that web site) But the good news might be that a portion of the spots are available starting the day before you enter the wilderness on a first-come, first-serve basis (again more info on the site). How far (distance, elevation gain) would your 5-year-old be able to hike? That may dictate your options. May Lake is just over a mile from the Old Tioga Rd trailhead and although swimming is not allowed, people have told me it is good for fishing. There is also a day hike from there up Mount Hoffman. A longer but easy, flat trail option would be heading up Lyell Canyon from Tuolumne Meadows but you have to go a few miles before you can camp. A less popular destination would be heading to Illilouette Canyon out of the Mono Meadow area but the mileage is also further than you posted about. All of these destinations would be beautiful but be prepared for lots of mosquitos this year at that time!