This is a Solsthiem "OTHER" quest, and apart from the first three gems and a rumor that someone might have one for sale I can find nothing else about it.

I stumbled into it by the usual means, but now I'm beginning to wonder. For the sake of it I looked at Wikipedia, but they have a link to a totally blank page as if they are aware of it, but have zero information either...

EDIT: Oops! Never mind - I found a link at www.uesp.wiki

The UESP is the best place for info on all TES related stuff.

For what it's worth, you only need four out of the five gems to get through the trials, and the reaver inside Kagrumez has two of em.