The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is 13 yards and the height is 5 yards. Plugging in the values:
\[ A = \frac{1}{2} \times 13 \times 5 \]
Calculating that:
\[ A = \frac{1}{2} \times 65 = 32.5 \text{ square yards} \]
So the area of the triangle is 32.5 square yards.