[tex]\log_5x-2\log_x 5=1\\
C.E.:x\in(0,\infty)-\{1\}\\
\log_5 x-\dfrac{2}{\log_5 x}=1\\
\log_5 x\stackrel{not}{=}t\\
t-\dfrac{2}{t}=1|\cdot t\neq 0\\
t^2-2=t\\
t^2-t-2=0\\
\Delta=1+8=9\Rightarrow \sqrt{\Delta}=3\\
t_1=\dfrac{1+3}{2}=\dfrac{4}{2}=2\\
t_2=\dfrac{1-3}{2}=\dfrac{-2}{2}=-1\\
i)\log_5x =2\Rightarrow x=25\\
ii)\log_5 x=-1\Rightarrow x=\dfrac{1}{5}\\
S=\left\{25,\dfrac{1}{5}\right\} [/tex]
