1. **State the problem:** We are given that $(a - b) = 5$ and $ab = 28$. We need to find the value of $a^3 - b^3$. 2. **Recall formula:** The difference of cubes can be factored as: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ 3. **Calculate $a^2 + ab + b^2$:** We know $ab = 28$ and $a - b = 5$. First, find $a^2 + b^2$ using the identity: $$ (a - b)^2 = a^2 - 2ab + b^2 $$ So, $$ 5^2 = a^2 - 2(28) + b^2 $$ $$ 25 = a^2 - 56 + b^2 $$ $$ a^2 + b^2 = 25 + 56 = 81 $$ Then, $$ a^2 + ab + b^2 = (a^2 + b^2) + ab = 81 + 28 = 109 $$ 4. **Calculate $a^3 - b^3$:** Using $$ a^3 - b^3 = (a - b)(a^2 + ab + b^2) = 5 imes 109 = 545 $$ **Final answer:** $a^3 - b^3 = 545$ which corresponds to option c.