1. **State the problem:** We need to square the binomial $\left(8y - 5\right)^2$. 2. **Formula used:** The square of a binomial $\left(a - b\right)^2$ is given by: $$\left(a - b\right)^2 = a^2 - 2ab + b^2$$ 3. **Apply the formula:** Here, $a = 8y$ and $b = 5$. $$\left(8y - 5\right)^2 = (8y)^2 - 2 \times 8y \times 5 + 5^2$$ 4. **Calculate each term:** $$= 64y^2 - 80y + 25$$ 5. **Final answer:** The expanded form of $\left(8y - 5\right)^2$ is: $$64y^2 - 80y + 25$$ 6. **Check options:** The correct choice is $64y^2 - 80y + 25$.