Tournament Bracket with Seating Constraints

In a round-robin chess mini-tournament, 5 players are randomly assigned to 5 boards (one player per board, all $5!$ assignments equally likely). The boards are numbered $1$ through $5$ in a circle, so board $6$ wraps to board $1$. Player $i$ has a "comfort zone" consisting of boards $i$ and $i{+}1$ (cyclically: player 5's comfort zone is $\{5, 1\}$). The organizer wants every player to be outside their comfort zone. Find $P(\text{no player is assigned to a board in their comfort zone})$.