9.086. $5^{2 \sqrt{x}}+5<5^{\sqrt{x}+1}+5^{\sqrt{x}}$.

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9.086. $5^{2 \sqrt{x}}+5<5^{\sqrt{x}+1}+5^{\sqrt{x}}$.
Solution.

Let's represent the given inequality as $\left(5^{\sqrt{x}}\right)^{2}+5<5 \cdot 5^{\sqrt{x}}+5^{\sqrt{x}}$, $\left(5^{\sqrt{x}}\right)^{2}-6 \cdot 5^{\sqrt{x}}+5<0$. Solving this inequality as a quadratic equation in terms of $5^{\sqrt{x}}$, we get $1<5^{\sqrt{x}}<5, \quad 0<\sqrt{x}<1, \quad 0<x<1$.

Answer: $\quad x \in(0 ; 1)$