On the floor that you mark as floor 1, you don't have to identify the the item and can just leave them on the floor. A relic will glow after 4 or 5 digs (i never counted) without identifying. This can save time if you want to go through the first 5 floor faster.
I suspected that might be the case, since I noticed the last relic always activated after I would check an item to begin identifying it, but before I actually finished the identification process, but I never bothered trying to see if it'd work that way. You still need to check the item, however, correct? I ran around and dug at a lot of glow spots, but in my one try, they didn't seem to activate any relics until I started checking items. Also, I never counted either, but they seem to require slightly more digs for each next relic. The first two always seem to activate very soon, and the last seems to take a bit longer.
Floor 5 in my example seems to behave the same.
So if you don't care for the items identifying it will get you, you can slightly speed up those floors.