1. **State the problem:** We are given $a=5$, $b=-2$, and $c=-3$. We need to find: (i) $5abc - a^2c$ (ii) $5b^2 - 3a - 2c$ 2. **Calculate (i) $5abc - a^2c$:** First, calculate each component: $$abc = 5 \times (-2) \times (-3) = 5 \times 6 = 30$$ Then: $$5abc = 5 \times 30 = 150$$ Next, calculate $a^2c$: $$a^2 = 5^2 = 25$$ $$a^2c = 25 \times (-3) = -75$$ Now substitute these values into the expression: $$5abc - a^2c = 150 - (-75) = 150 + 75 = 225$$ 3. **Calculate (ii) $5b^2 - 3a - 2c$:** Calculate $b^2$: $$b^2 = (-2)^2 = 4$$ Multiply by 5: $$5b^2 = 5 \times 4 = 20$$ Calculate $-3a$: $$-3a = -3 \times 5 = -15$$ Calculate $-2c$: $$-2c = -2 \times (-3) = 6$$ Now sum all terms: $$5b^2 - 3a - 2c = 20 - 15 + 6 = 11$$ **Final answers:** (i) $5abc - a^2c = 225$ (ii) $5b^2 - 3a - 2c = 11$