1. **State the problem:** We have a right triangle with legs of lengths 5 yards and 12 yards, and we want to find the length of the hypotenuse $c$. 2. **Formula used:** According to the Pythagorean theorem, for a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship is: $$c^2 = a^2 + b^2$$ 3. **Apply the formula:** Here, $a = 5$ yards and $b = 12$ yards, so: $$c^2 = 5^2 + 12^2$$ 4. **Calculate squares:** $$c^2 = 25 + 144$$ 5. **Add the values:** $$c^2 = 169$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{169}$$ 7. **Simplify the square root:** $$c = 13$$ 8. **Conclusion:** The length of the hypotenuse $c$ is 13 yards. No rounding is necessary since 13 is an integer.