I don't know how plumbing works, but I think this would work:

I'd empty the hair from my hairbrush, tangle the paperclip in it and put the clump down my shower drain. Hair clump keeps it from draining away keeping it "in my house." Retrieve after with one of those spikey stick snake things. Spend the remaining 3 minutes touching other hiding places to throw the detective off the scent.

If that doesn't count as in the house I'd probably just slip it into a pocket of a coat in my closet. I doubt they'd think to check every pocket of every item of clothing. They're probably checking all the vents and window panels and little holes in my walls, and I don't think they'd catch me because I go in my closet a lot so it's not like I've disturbed dust to go in there during the 5 minutes.