Let the cost of each sports book be \( x \). Since Mitch bought four sports books, the total cost for the sports books would be \( 4x \).
The novel costs \( x - 7 \) (as it costs $7 less than each sports book).
So, the total cost of all five books can be expressed as:
\[ 4x + (x - 7) = 68.75 \]
This simplifies to:
\[ 4x + x - 7 = 68.75 \]
\[ 5x - 7 = 68.75 \]
Now, add 7 to both sides:
\[ 5x = 68.75 + 7 \]
\[ 5x = 75.75 \]
Now, divide by 5:
\[ x = \frac{75.75}{5} \]
\[ x = 15.15 \]
Thus, the cost of each sports book is $15.15.