1. **State the problem:** We want to find the derivative with respect to $x$ of the function $$f(x) = \int \frac{(x^3 - x^8)^5}{x^{-3}} \, dx.$$ 2. **Simplify the integrand:** Recall that dividing by $x^{-3}$ is the same as multiplying by $x^3$. So, $$\frac{(x^3 - x^8)^5}{x^{-3}} = (x^3 - x^8)^5 \cdot x^3.$$ 3. **Rewrite the function:** $$f(x) = \int (x^3 - x^8)^5 x^3 \, dx.$$ 4. **Differentiate the integral:** By the Fundamental Theorem of Calculus, if $F(x) = \int g(x) \, dx$, then $\frac{d}{dx}F(x) = g(x)$. Here, the integrand is the function inside the integral, so $$\frac{d}{dx} f(x) = (x^3 - x^8)^5 x^3.$$ 5. **Final answer:** $$\boxed{\frac{d}{dx} \int \frac{(x^3 - x^8)^5}{x^{-3}} \, dx = (x^3 - x^8)^5 x^3}.$$