Answer
x-intercept: $(-20, 0)$
y-intercept: $(0, 16)$
Work Step by Step
To find the x-intercept, set $y=0$ then solve for $x$:
$-4x+5y=80
\\-4x+5(0)=80
\\-4x=80
\\\frac{-4x}{-4}=\frac{80}{-4}
\\x=-20$
Thus, the x-intercept of the graph of the given equation is $(-20, 0)$.
To find the y-intercept, set $x=0$ then solve for $y$:
$-4x+5y=80
\\-4(0)+5y=80
\\5y=80
\\\frac{5y}{5}=\frac{80}{5}
\\y=16$
Thus, the y-intercept of the graph of the given equation is $(0, 16)$.