If I never see the guy again, never play the game again (basically the problem postulated), I take any offer. But I absolutely don't let him know that ahead of time. Even if he gives me $0, I'll let him have all $5000. Unless that money came from a charity to feed orphans or something.
Good point. This game is designed so that the people discussing it will have a tendancy to lie about how they would really act: Potential players discussing the game are incentivized to provide the
appearance that they would deny small values of money, but are incentivized to accept all values of money when they are actually in the situation.