Solve $\frac{5-2x}{3} \leq \frac{x}{6}-5$.

(N/A) We have $\frac{5-2x}{3} \leq \frac{x}{6}-5$.
Multiply both sides by $6$ to clear the denominators:
$2(5-2x) \leq x - 30$
$10 - 4x \leq x - 30$
Subtract $x$ from both sides:
$10 - 5x \leq -30$
Subtract $10$ from both sides:
$-5x \leq -40$
Divide by $-5$ (remembering to reverse the inequality sign when dividing by a negative number):
$x \geq 8$
Thus,the solution set is $x \in [8, \infty)$.