1. Problem: Given $x - 5 = -8$, evaluate $(x^2 - 5)(x^{-3} - x)$. 2. First, solve for $x$: $$x - 5 = -8$$ Add 5 to both sides: $$x - 5 + 5 = -8 + 5$$ $$x = -3$$ 3. Substitute $x = -3$ into the expression: $$(x^2 - 5)(x^{-3} - x) = ((-3)^2 - 5)((-3)^{-3} - (-3))$$ 4. Calculate each part: $$(-3)^2 = 9$$ So, $$9 - 5 = 4$$ 5. Calculate $(-3)^{-3}$: $$(-3)^{-3} = \frac{1}{(-3)^3} = \frac{1}{-27} = -\frac{1}{27}$$ 6. Calculate $(-3)^{-3} - (-3)$: $$-\frac{1}{27} - (-3) = -\frac{1}{27} + 3 = 3 - \frac{1}{27} = \frac{81}{27} - \frac{1}{27} = \frac{80}{27}$$ 7. Multiply the two results: $$4 \times \frac{80}{27} = \frac{320}{27}$$ 8. Final answer: $$(x^2 - 5)(x^{-3} - x) = \frac{320}{27}$$