9.203. $5^{\log _{5}^{2} x}+x^{\log _{5} x}<10$.
Solution.

Domain of definition: $x>0$.

Rewrite the inequality as

$5^{\log _{5} x \log _{5} x}+x^{\log _{5} x}<10 \Leftrightarrow x^{\log _{5} x}+x^{\log _{5} x}<10 \Leftrightarrow$

$\Leftrightarrow 2 x^{\log _{5} x}<10, x^{\log _{5} x}<5$. Taking the logarithm of both sides of this inequality to the base 5, we get $\log _{5} x \log _{5} x<\log _{5} 5, \log _{5}^{2} x<1$, $-1<\log _{5} x<1, \frac{1}{5}<x<5$.

Answer: $x \in\left(\frac{1}{5} ; 5\right)$.