Crap! Ac ok? These 5.3 engines are just famous for mystery H20 leaks and most of the time it's the pump or rad. A little unusual for the core to leak. When you get it fixed use good old fashion antifreeze, not Dexcool.
That is just a bunch of B.S.!! After working on these GM vehicles and seeing the effect of Dexcool, first thing i did, after warranty, on my Blazer is flush that crap out and replace it with the old green stuff. Google Dexcool, look around a bit and you will see, i think. Probably the reason your heater core is leaking!