ĐK: $x>0$.
Bất phương trình tương đương với:
$\dfrac{\ln x}{\ln 3}-\dfrac{\ln x}{\ln 5}\le\dfrac{\ln x}{\ln 3}.\dfrac{\ln x}{\ln 5}$
$\Leftrightarrow \ln 5\ln x-\ln 3\ln x\le\ln^2x$
$\Leftrightarrow \ln x(\ln x+\ln 3-\ln 5)\ge0$
$\Leftrightarrow \ln x\ln\dfrac{3x}{5}\ge0$
$\Leftrightarrow \left[\begin{array}{l}\ln x=0\\\ln\dfrac{3x}{5}=0\\\left\{\begin{array}{l}\ln x<0\\\ln\dfrac{3x}{5}<0\end{array}\right.\\\left\{\begin{array}{l}\ln x>0\\\ln\dfrac{3x}{5}>0\end{array}\right.\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x=1\\x=\dfrac{5}{3}\\\left\{\begin{array}{l}0<x<1\\0<x<\dfrac{5}{3}\end{array}\right.\\\left\{\begin{array}{l}x>1\\x>\dfrac{5}{3}\end{array}\right.\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}0<x\le 1\\x\ge\dfrac{5}{3}\end{array}\right.$