Why not just have #5 play the other #5 in the league, 1 home, 1 away?
this already happens. The point is there is no revenue from that game.
I keep to my solution to have relegation games become no-revenue games as well, it would solve the entire situation. It is prety simple this way as well.
They are not your friends; they dispise you. I am the only one you can count on. Trust me.