5 teams compete against each other only once the probability that a team wins all four of its games and the other team loses all 4 of its games
Think in terms of 'league table' listing the number of wins, draws, and losses for each team. Be aware that each one of 5 teams has played 4 games since each team has four opposing teams.
One such possible 'league table' could look like:
W D L
4 0 0 --> 4 wins
1 2 1
1 2 1
1 2 1
0 0 4 --> 4 losses
Take it from there.