We are asked to find the values of $x$ for which the expression $\frac{x-4}{5x-40} \div \frac{x-1}{x+5}$ is undefined.

1. Problem Description

We are asked to find the values of $x$ for which the expression $\frac{x-4}{5x-40} \div \frac{x-1}{x+5}$ is undefined.

2. Solution Steps

A rational expression is undefined when the denominator is equal to zero. Also, when dividing fractions, we multiply by the reciprocal, so the numerator of the second fraction becomes a denominator. Therefore, the expression is undefined when $5x-40=0$, $x+5=0$, or $x-1=0$.

First, we solve $5x-40 = 0$:

$5x = 40$

$x = \frac{40}{5}$

$x = 8$

Next, we solve $x+5 = 0$:

$x = -5$

Finally, we solve $x-1 = 0$:

$x = 1$

Thus, the expression is undefined when $x = 8$, $x = -5$, or $x = 1$.

3. Final Answer

The expression is undefined when $x = -5, 1, 8$.