The formula for the area \( A \) of a triangle is given by:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For a triangle with a base of 13 yards and a height of 5 yards, we can substitute these values into the formula:
\[ A = \frac{1}{2} \times 13 \times 5 \]
Calculating this gives:
\[ A = \frac{1}{2} \times 65 = 32.5 \]
Therefore, the area of the triangle is 32.5 square yards.