Lior: Bava Kama 27. We Pasken in the Shulchan Aruch that it is Muttar but only in a case where there is absolutely no question that you would win this dispute in court. In this case, since there is no proof that would win in a Beis Din, it is Assur.
DY: Your logic about no particular $5 bill being yours is false because money is fungible.