Also, there's actually a way to win as the receiver if there is communication. If you can make a binding decision ahead of time, you could say "I will reject any offer less than $4990".
If you can make such a
binding decision you are effectively reversing the roles. You are now the one calling the quantity and the other guy is the one that only gets to accept or veto. From your perspective, you are not playing, and therefore not winning, the original game.
In the problem as formulated, you
cannot make such a binding decision.
Now, imagine you could make a non-binding declaration of how much you will accept, and that the other guy offers you $10 nevertheless. Does that change your choice?
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.