What it boils down to is, that 5% increase isn't going to increase something with a 1% drop rate to 6%, it's going to increase it to 1.05%. Obviously this is scaled to whatever the actual drop rates of the Legendary weapon you're searching for may be.
Equally so, AFAIK, it increases the drop rates of Blue/Purple, and possibly Green rarity items. So while Orange items get ever so slightly higher drop rates, lower grades down to white and/or Green items are increased as well.
Furthermore, at least originally, the relic was completely bugged and did literally nothing at all. It was just completely useless; People also edited it's values up from 5% to ridiculous numbers, and it didn't make any difference at all.
So, even assuming the bug of it doing *nothing*, the Relic is a complete waste. It does nothing significant enough to warrant using the Relic slot, in place of the many other infinitely more useful relics that are out there.