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I recommend the Great Smoky Mountains Railroad. That's a major attraction in Dillsboro. The train doesn't go fast or anything, but they have open air cars and it's pretty fun. The trips are about 4 hours long, so if the 5 year olds tend to get restless, bring some sort of game along to play with them.
In addition to rafting, I also recommend tubing at Deep Creek in nearby Bryson City. Just start driving out Deep Creek Road and you'll pass half a dozen places to rent tubes for a couple bucks each.
There are lots of trails in the Smokies for hikers of all skill levels, though many of them are only accessed by long winding dirt roads. I recommend you explore the higher elevations if it's particularly hot.
You could also do my favorite hike in NC, the Horsepasture River - near Cashiers. It's not too tough, and it can't be beat for "impressive waterfalls per mile hiked." Google says it's a 1hr drive from Dillsboro. While you're out there you could stop by Highlands, a neat 1920s era resort town.
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