5 teams in the tournament.
3 teams play in each game.
6 games are played by each team.
10 games are played in the whole tournament.
Each team plays every other team 3 times.
Each team plays on every colour twice.

Game
ABCDEFGHIJ
Team1R Y G GR Y
2GR Y R Y G
3 GR YY GR
4Y GR GR Y
5 Y GR Y GR

To use this grid in a league, you'd probably want to break it up over two weeks: play games A to E on the first week, and games F to J on the second. Then shuffle the teams and run it again. The following would be a good shuffle rule:
1 to 2, 2 to 4, 3 to 1, 4 to 3, 5 to 5.

4 team Tournament Grids 6 team tournament
League Grids 6 team league