I'd just keep it.
You say "How would you feel if you lost $5000", but I wouldn't be stupid enough to be carting around $5000 in the first place and magically lose it.
The most money I've ever had on me at one time was $800. I put it in my front pants pocket, then put my hands in my pocket so I was holding the money the whole time (I was buying a laptop).
Whenever I carry more money than usual, I make sure I'm always holding it while it's in some other protection (like a pocket, or a case)
And as for "Someone will eventually report the money missing", well for all you know, someone could've overheard you in the police department saying you found money, and then call in and try to report it as theirs.