The problem asks for the slope of the line perpendicular to the line given by the equation $8x - 5y = 40$.

1. Problem Description

The problem asks for the slope of the line perpendicular to the line given by the equation $8x - 5y = 40$.

2. Solution Steps

First, we need to find the slope of the given line. To do this, we can rewrite the equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

$8x - 5y = 40$

$-5y = -8x + 40$

$y = \frac{-8}{-5}x + \frac{40}{-5}$

$y = \frac{8}{5}x - 8$

So the slope of the given line is $\frac{8}{5}$.

The slope of a line perpendicular to a line with slope $m$ is $-\frac{1}{m}$. Therefore, the slope of the perpendicular line is:

$m_{\perp} = -\frac{1}{\frac{8}{5}} = -\frac{5}{8}$

3. Final Answer

The slope of the line perpendicular to the line $8x - 5y = 40$ is $-\frac{5}{8}$.

The answer is (A).