To find the cost per player, we can follow these steps:
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First, determine the total amount collected from the players. Since there are 60 players and each pays $5:
\[ \text{Total amount from players} = 60 \times 5 = 300 \text{ dollars} \]
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Next, we can find out how much the league has to pay by subtracting the amount collected from the total cost of the banquet:
\[ \text{League's contribution} = \text{Total cost} - \text{Total amount from players} = 960 - 300 = 660 \text{ dollars} \]
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Now, since the question specifically asks for the cost per player of the banquet, we consider the total cost of the banquet divided by the number of players:
\[ \text{Cost per player} = \frac{\text{Total cost}}{\text{Number of players}} = \frac{960}{60} = 16 \text{ dollars} \]
Thus, the cost per player for the banquet is $16.