1. **Evaluate the indefinite integral** $\int (x^3 + 5) \, dx$. 2. The integral of a sum is the sum of the integrals: $$\int (x^3 + 5) \, dx = \int x^3 \, dx + \int 5 \, dx$$ 3. Use the power rule for integration: for any $n \neq -1$, $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ and the integral of a constant $a$ is $$\int a \, dx = ax + C$$ 4. Applying the power rule: $$\int x^3 \, dx = \frac{x^{3+1}}{3+1} = \frac{x^4}{4}$$ and $$\int 5 \, dx = 5x$$ 5. Combine the results: $$\int (x^3 + 5) \, dx = \frac{x^4}{4} + 5x + C$$ where $C$ is the constant of integration. **Final answer:** $$\boxed{\frac{x^4}{4} + 5x + C}$$