To represent the total cost for a customer who purchases \( w \) car washes, you can express it with the following formula:
\[ \text{Total cost} = 14w + 5 \]
In this expression:
- \( 14w \) represents the charge for car washes, where \( w \) is the number of washes purchased.
- \( 5 \) is the one-time fee for supplies.
Now, for the total cost of 10 washes, you would substitute \( w \) with \( 10 \):
\[ \text{Total cost for 10 washes} = 14(10) + 5 = 140 + 5 = 145 \]
Thus, the total cost for 10 washes is $145.