The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is 13 yards and the height is 5 yards. Plugging in these values, we get:
\[ \text{Area} = \frac{1}{2} \times 13 \times 5 \]
Calculating this:
\[ \text{Area} = \frac{1}{2} \times 65 = 32.5 \text{ square yards} \]
So the area of the triangle is 32.5 square yards.