Let the fee to rent each pair of shoes be denoted as \( x \).
Ben's group spent a total of $37, which includes the fee for bowling and the rental fees for the shoes. The bowling alley charges $22 for an hour of group bowling. Since Ben's group rented 5 pairs of shoes, the total rental cost for the shoes would be \( 5x \).
We can set up the equation based on the total amount paid:
\[ 22 + 5x = 37 \]
Next, we need to isolate \( x \). First, we can subtract 22 from both sides of the equation:
\[ 5x = 37 - 22 \]
This simplifies to:
\[ 5x = 15 \]
Now, divide both sides by 5 to solve for \( x \):
\[ x = \frac{15}{5} = 3 \]
Thus, the fee to rent each pair of shoes is
\[ \boxed{3} \]