re: Are the trails at Tunica Hills safe for kids? I have a 5 and 7 year old.

The key is keeping them on the trails. Don't lay out a blanket and fall asleep while they run around on the cliffs. Supervise your kids. They and you will have a blast. Like Dirty Mike said, slather them up with bug spray before you go, because he is right about the ticks. This is the perfect time of year to go, before all the poison ivy is out in full, but there may be some still present so be mindful.
I was taking my kid out there at 7 or 8 years old but always see people with younger ones. You may have to carry the 5 year old out if they get tired. As Liz said the country store is a must too. Moon pies and a Gatorade or soda pop after the hike.