Two at the Arcane University – one in the lobby of the Arch-Mages Tower and one in the Mages Quarters.
Two more are in a five-tumbler display case on the ground floor of the Chorrol Mages Guild. Where can I find 5 empty grand soul gems? If you take a stack of soul gems (more than 8 is a stack) and give them to a companion with a soul trap weapon (it’s is best to give them a bow and melee weapon so they don’t mess it up), when they kill something, it will fill the entire stack of soul gems. What is the fastest way to fill soul gems? You can do this by casting the Soul Trap skill (from the Soul Magic skill line) on an enemy before killing it. If a soul gem is empty, you will need to fill it before it can be used. Soul gems may be found in loot or purchased from vendors, and they may be either empty or full. If you feel like doing an instanced dungeons over and over again, you can do that and you will get a lot of Soul Gems by clearing them a lot of times. One of the ways to get a lot of Soul Gems in your possession is by defeating the bosses of every dungeon available in the game.