1. **State the problem:** Find the perpendicular distance from the point $P(5, -2)$ to the line given by the equation $$y = \frac{4}{3}x - 11.$$ 2. **Formula used:** The distance $d$ from a point $(x_0, y_0)$ to a line $Ax + By + C = 0$ is given by: $$d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}.$$ 3. **Rewrite the line in standard form:** Given $$y = \frac{4}{3}x - 11,$$ multiply both sides by 3 to clear the fraction: $$3y = 4x - 33.$$ Bring all terms to one side: $$4x - 3y - 33 = 0.$$ So, $A = 4$, $B = -3$, and $C = -33$. 4. **Substitute the point coordinates into the formula:** $$d = \frac{|4(5) - 3(-2) - 33|}{\sqrt{4^2 + (-3)^2}} = \frac{|20 + 6 - 33|}{\sqrt{16 + 9}} = \frac{|-7|}{\sqrt{25}} = \frac{7}{5}.$$ 5. **Interpretation:** The perpendicular distance from the point $(5, -2)$ to the line $y = \frac{4}{3}x - 11$ is $$\boxed{\frac{7}{5}}$$ or 1.4 units.