Culling is putting birds down. Sometimes it becomes necessary to do so in the case of chronically ill birds or to protect the greater good of the flock.
For treating your barred rock, I'd probably go with the Tylan 50. Whatever you get it's always best to dose the bird directly, either orally...
First, one question: When you say you "let them all out with the others..." did you already have some birds at home that you integrated these 5 new ones with?
As for treatment....dust all your new birds for mites/lice. If the barred rock has them and they all came from the same place then...