# 5. Solution:

$\frac{-2\left(x^{2}-5 x+25\right)\left(2 x^{2}+17 x+35\right)}{\left(x^{3}+125\right) \sqrt{4 x^{2}+28 x+49}} \leq x^{2}+3 x-2 . \Leftrightarrow \frac{-2\left(x^{2}-5 x+25\right)(x+5)(2 x+7)}{(x+5)\left(x^{2}-5 x+25\right) \sqrt{(2 x+7)^{2}}} \leq x^{2}+3 x-2 \Leftrightarrow$

$x \neq-5, \frac{-2(2 x+7)}{|2 x+7|} \leq x^{2}+3 x-2 \Leftrightarrow\left[\begin{array}{l}\left\{\begin{array}{l}x \in(-3.5 ;+\infty), \\ x^{2}+3 x \geq 0,\end{array}\right. \\ \left\{\begin{array}{l}x \in(-\infty ;-5) \cup(-5 ;-3.5), \\ x^{2}+3 x-4 \geq 0 .\end{array}\right.\end{array} \Leftrightarrow\right.$

$x \in(-\infty ;-5) \cup(-5 ;-4] \cup(-3.5 ;-3] \cup[0 ;+\infty)$.
Answer: $x \in(-\infty ;-5) \cup(-5 ;-4] \cup(-3.5 ;-3] \cup[0 ;+\infty)$.