Let \( r \) represent the cost of the red shirt. According to the problem, the blue shirt costs $13, which is $2.50 more than the red shirt. This can be expressed with the following equation:
\[ 13 = r + 2.50 \]
To solve for \( r \), we can subtract $2.50 from both sides of the equation:
\[ 13 - 2.50 = r \]
Calculating the left side:
\[ 10.50 = r \]
Therefore, the cost of the red shirt is:
\[ \boxed{10.50} \]