I would take a gallon milk jug filled with water out to the approximated 250-300yds. and see if I could hit it 5 times.
Is it a possibility you hit close to the skunk causing dirt/ rocks to hit him making him jump?
I've used various LR .22 ammo (Stingers included) on varmints and even a couple yotes around the farm here. Ranges out to 45-50yds. if I do my part, I've not seen that big a difference in the terminal effects on game when using most of the majors brands(CCI,Winchester,Rem., Aguila, etc) with the same cartridge recipe of ingredients. IE: bullet grn. weight, powder charge, similar primer, etc...
...but 45-50yds. is a sight closer then 250-300yds
Five hits on a skunk @ that yardage is some good shootin.