Chapter 9 - Polar Coordinates; Vectors - 9.5 The Dot Product - 9.5 Assess Your Understanding - Page 617: 49

$12$

General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$ Hence here: $\frac{f(2)-f(-3)}{2-(-3)}=\frac{(2^3-5\cdot2^2+27)-((-3)^3-5\cdot(-3)^2+27)}{5}=\frac{(8-20+27)-(-27-45+27)}{5}=\frac{15-(-45)}{5}=\frac{60}{5}=12.$