To solve the compound inequality $5 - 3x \leq -1$ or $8 + 2x \leq 5$, solve each inequality individually. For the first inequality, subtracting 5 yields $-3x \leq -6$, and dividing by -3 (which reverses the inequality sign) gives $x \geq 2$. For the second inequality, subtracting 8 yields $2x \leq -3$, and dividing by 2 gives $x \leq -\frac{3}{2}$. Graphing these solutions reveals that $x \geq 2$ is a region shaded to the right of a bracket at 2, while $x \leq -\frac{3}{2}$ is a region shaded to the left of a bracket at $-\frac{3}{2}$. The solution to the 'or' compound inequality is the union of these two graphs, which consists of all numbers that satisfy either condition. In interval notation, this combined solution is written as $(-\infty, -\frac{3}{2}] \cup [2, \infty)$.