To simplify the expression $\frac{x - 5}{x^3 - 2x^2 - 11x - 20}$, we can start by factoring the cubic polynomial in the denominator, if possible.

Step 1: Factor the denominator

We are looking to factor: $x^3 - 2x^2 - 11x - 20$ Using the Rational Root Theorem, we test possible rational roots such as $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$.

Let's start by checking $x = -4$:

$(-4)^3 - 2(-4)^2 - 11(-4) - 20 = -64 - 32 + 44 - 20 = -72$ This is not zero, so $x = -4$ is not a root.

Now, let's check $x = -2$:

$(-2)^3 - 2(-2)^2 - 11(-2) - 20 = -8 - 8 + 22 - 20 = -14$ So $x = -2$ is not a root.

We will divide the polynomial