Each player will pay five dollars to attend the banquet for their soccer league in the league will pay the rest of the cost. The total cost for the banquet is $960 if there are 60 players in the league find the cost per player.
The total cost of the banquet is $960 and there are 60 players in the league. Each player is required to pay $5.
The total amount paid by the players is 60 x $5 = $<<60*5=300>>300.
The remaining cost to be paid by the league is $960 - $300 = $<<960-300=660>>660.
The cost per player, paid by the league, is $660 / 60 players = $<<660/60=11>>11 per player. Answer: \boxed{11}.