To work it out...
Player 1 will play players: 2, 3, 4, 5
Player 2 will play players: 3, 4, 5
Player 3 will play players: 4, 5
Player 4 will play players: 5
All of player 5's matches have already been mentioned
Therefore, in answer to your question, I think 10 matches will be played.
Hope this helps.