For safety's sake and the sake of your children I'd replace them. The tires are 5 years old and have probably used up a good portion of their lifespan(not sure what these tires were originally rated at for mileage.) Why risk it when you could have "peace of mind" knowing that replacing the tires will get rid of the "blowout, or other tire problem(s)" thoughts.
There have been thoughts recently on how long tires do last and under what circumstances they should be replaced. Below is a small section of article on this matter:
"While American driving conditions don't include the high-speed challenges of the German Autobahn, the U.S. divisions of DaimlerChrysler and Ford Motor Company joined their European colleagues in 2005 by recommending the tires installed as Original Equipment be replaced after six years of service. (General Motors declined to offer a recommendation until a more scientific analysis of driving conditions and tire aging could be completed)."
The link to the full article is here -->
http://www.tirerack.com/tires-techpage-1/138.shtml
If you follow the recommendations of some OEM manufacturers the tires are almost to the end of their useful life. It would probably be cheaper to replace the tires than to have an incident with them and incur damage not only to your vehicle but to the lives of anybody in the vehicle.