Answer
$(-∞, -2) U (1, 2) $
Work Step by Step
$\frac{5}{x^3 - x^2 - 4x + 4} < 0$
Find the zeros of the expressions in the numerator AND the denominator
$\frac{5}{x^2 (x - 1) - 4 (x-1)} < 0$
$\frac{5}{(x^2 - 4) (x-1)} < 0$
$\frac{5}{(x+2) (x-1) (x-2)} < 0$
x = -2, 1, 2
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -2) $\frac{(+)}{(-)(-)(-)} = (-)$
(-2, 1) $\frac{(+)}{(+)(-)(-)} = (+)$
(1, 2) $\frac{(+)}{(+)(+)(-)} = (-)$
(2, ∞) $\frac{(+)}{(+)(+)(+)} = (+)$
Thus the solution is $(-∞, -2) U (1, 2) $
