I have been pulling a 7880 GVWR trailer with a 2001 5.4 for more than a decade. Been over the Rockies, Sierras, Siskiyou and plenty more. Yes it slows a bit with grade and elevation. Slowing down is not inherently unsafe.
I did swap in some 4.10 ratio gears to keep the RPM up a bit.
In general I recommend keeping the trailer GVWR within the tow rating. If close do not expect to load a bunch of heavy items in the tow vehicle.
Probably fine if you are patient. For many a newer and more capable vehicle will give a better experience.