Every 12 hours or something like that, at least once daily for sure, talk to the dreamer in whatever town you accepted the quest in to get an egg. Trade with other players to get a regular Archon Egg, and one each of earth, lightning, and water. Then talk to one of the quest NPCs again to exchange them for a Pristine Egg Cap. I don't know how to get the other caps, but that's how you finish the R5 quest.