To find the integral of $(x-5)^5$, we can apply the power rule for integration.

$\int (x - 5)^5 \, dx$

Let’s use the substitution method. Let $u = x - 5$. Then $du = dx$.

Now, the integral becomes:

$\int u^5 \, du$

Using the power rule:

$\int u^5 \, du = \frac{u^6}{6} + C$

Substituting back $u = x - 5$:

$\frac{(x - 5)^6}{6} + C$

So, the integral is:

$\int (x - 5)^5 \, dx = \frac{(x - 5)^6}{6} + C$

Would you like more details or have any questions on this?

Here are some related questions:

1. What happens if the exponent is negative in the integral?
2. How do you evaluate definite integrals?
3. What is the power rule for integration?
4. What is the general method for solving integrals by substitution?
5. How do you apply the chain rule to integrals?

Tip: Always look for substitution opportunities to simplify the integral before applying power rules.