1000s and 1000s of trailers never have a blow out. Just because some do that doesn't mean you will. Its easy to get caught up in all the ST fear mongering.
Sure there are some really bad ones made. But it's the same with anything.
I've put over 20,000 miles on two sets of ST tires. Just because someone else had a blowout doesn't mean I will.
My questions are
How much do you tow?
What size tires do you have?
What brand?
What's the loaded weight of the trailer?
And what's the max load for the ST tires?
If you only tow a couple 1000 miles a year or less and your tires aren't maxed out, then if it were me I'd run them.
If you're maxed out on the tires, then upgrade to a higher rated tire.
If they're some weird brand that you have trouble saying then I'd up grade.
If they're a known decent brand and you meet the weight and miles limits then I'd keep em till they are used up somewhat.
The only sure fire way you're going to avoid blowouts is to upgrade to LT tires. But since you trailer is only 5000lbs loaded then it's highly doubtful that you'll find LT tires that will fit.
One more thing. Keep your speed under 65mph.