7.188. $\sqrt{\log _{5}^{2} x+\log _{x}^{2} 5+2}=2.5$.
## Solution.

Domain of definition: $00, \\ \log _{5}^{2} x-2.5 \log _{5} x+1=0\end{array} \Rightarrow\left(\log _{5} x\right)_{3}=\frac{1}{2}>0,\left(\log _{5} x\right)_{4}=2>0\right.$, from which $x_{3}=\sqrt{5}, x_{4}=25$.

Answer: $\frac{1}{25} ; \frac{1}{\sqrt{5}} ; \sqrt{5} ; 25$.