9.061. $25^{x}<6 \cdot 5^{x}-5$.
## Solution.

By writing the inequality as $\left(5^{x}\right)^{2}-6 \cdot\left(5^{x}\right)+5<0$ and solving it as a quadratic equation in terms of $5^{x}$, we get $1<5^{x}<5$, from which we find $0<x<1$.

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