What Must Be Found

If you're at 5/5 and can't complete the quest, I think what causes that is that you already found some before and turned them in. I had found just one (the talisman) but I got 2/5 progress upon accepting the quest. However, I wasn't able to turn it in at 5/5 and I had to go look at all the items before it said "Objective Completed" and I was able to turn it in. Just follow the top comment and go around the room until you're sure you've clicked them all.

There are several items in the room you need to inspect them:

Counterclockwise:

1. 
   
2. Singing Steel Ingot - to the left of questgiver
3. 
   
4. Celestial Shadowlands Chart - on the table
5. 
   
6. Rune Chit - same table
7. 
   
8. Talisman of the Eternal Scholar - behind the questgiver
9. 
   
10. Book of Binding: The Mad Witch - Near the Assistant Scholar Kah-Vez- Item Upgrade NPC
11. 
    

/way 62.53 22.68 Singing Steel Ingot
/way 62.64 23.18 Celestial Shadowlands Chart
/way 62.64 23.18 Rune Chit
/way 63.12 23.00 Talisman of the Eternal Scholar
/way 62.60 21.84 Book of Binding: The Mad Witch

Quest video: https://www.youtube.com/watch?v=wHVugvSD28I

If you ran out, the quest items are right there in the room where the archivist is.

/way 61.8 21.8 entrance