Olivia filled 4 baskets of apples, and her friend filled 1 additional basket. This means there are a total of:
\[ 4 + 1 = 5 \text{ baskets} \]
The total revenue from selling all the baskets is $160. To find the cost of each basket, we can divide the total amount earned by the number of baskets:
\[ \text{Cost per basket} = \frac{\text{Total Revenue}}{\text{Number of Baskets}} = \frac{160}{5} = 32 \]
Therefore, each basket of apples cost $32.