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What is the slope of a line perpendicular to the line whose equation is (x/4)-(y/5)=1? Express your answer as a common fraction.

We have this equation: $\frac{x}4-\frac{y}5=1$

Subtract ${x \over 4}$ from both sides: $-{y \over 5} = 1 - {x \over 4}$

Multiply the entire equation by -5: $y = {5 \over 4} x - 5$

This means that the slope is ${5 \over 4}$, the slope of the line that is perpendicular to this is the negative reciprocal, or $\color{brown}\boxed{-{4 \over 5}}$