$y=\dfrac{x^3+mx-1}{5x^5}$
$y'=\dfrac{(3x^2+m).5x^5-25x^4(x^3+mx-1)}{25x^{10}}=\dfrac{-10x^7-20mx^5+25x^4}{25x^{10}}=\dfrac{-2x^3-4mx+5}{5x^6}$
ĐK: $y'\ge 0\forall x>0$
$\to -2x^3-4mx+5\ge 0\forall x>0$
$\to 4mx\le -2x^3+5\forall x>0$
$\to m\le \dfrac{-2x^3+5}{4x}\forall x>0$
$\to m\le \min\limits_{(0;+\infty}\dfrac{-2x^3+5}{4x}$
$\to$ không có $m$ TM