To solve this inequality, we first need to find the critical points where the expression is equal to zero.

Set each factor equal to zero and solve for x:

(-5x - 2) = 0
-5x = 2
x = -2/5

(2 - 3x) = 0
-3x = -2
x = 2/3

(-x - 5) = 0
-x = 5
x = -5

Now, we determine the sign of each factor in the intervals created by these critical points (-5, -2/5, 2/3, -5).

Test interval (-∞, -5):
(-)(-)(-) = -
Therefore, the expression is negative in this interval.

Test interval (-5, -2/5):
(-)(-)(-) = -
Therefore, the expression is negative in this interval.

Test interval (-2/5, 2/3):
(-)(+)(-) = +
Therefore, the expression is positive in this interval.

Test interval (2/3, ∞):
(-)(+)(+) = -
Therefore, the expression is negative in this interval.

Finally, we consider the case where the expression is equal to zero:

(-x - 5) = 0
x = -5

So, the solution to the inequality is x ∈ (-∞, -5] ∪ [-2/5, 2/3].