I have never collected enough dropped set pieces to ever make a meaningful set, much less a 5 piece. The only exception to this is L15 to L23 Warlock, and that is because I farmed Guild Kiosks on my Vets. I now have a full 5 piece set at L15/16 and L20/23. While I have L23 Blue Jewelry, I can't seem to find anything above L20 for the clothing. This is for Blue or Dungeon Boss drops, there might be some Green Clothing I have that is higher than L20 but I don't remember if I have found any.
Anyway, back to your question. If you plan on using the gear on your next character while they level, then hand it to a mule character and let them carry it until then. Otherwise, decon or research it or sell it in the guild stores. In fact, you could probably make the full set by farming the Guild Kiosks yourself to acquire the pieces you don't have.
Low-level gear is generally not worth hanging onto.
The only exceptions, at least in my opinion, which undoubtedly varies from others', would be Night Mother pieces that drop in the lvl 16-22 zones. The reason for this is because it greatly improves stealth capabilities and is very useful for anything related to Legerdemain. With the pending release of the Thieves Guild, I believe these sets will still be of great value. (Note: a lot of vr16 characters use these level 22ish sets when they're doing their sneaky business, so in case you were wondering if they are relevant to high characters, the answer is yes.)
would be Night Mother pieces that drop in the lvl 16-22 zones. The reason for this is because it greatly improves stealth capabilities and is very useful for anything related to Legerdemain. With the pending release of the Thieves Guild, I believe these sets will still be of great value. (Note: a lot of vr16 characters use these level 22ish sets when they're doing their sneaky business, so in case you were wondering if they are relevant to high characters, the answer is yes.)