9.077. $2^{x+2}-2^{x+3}-2^{x+4}>5^{x+1}-5^{x+2}$.
Solution.

We have

$$
\begin{aligned}
& 4 \cdot 2^{x}-8 \cdot 2^{x}-16 \cdot 2^{x}>5 \cdot 5^{x}-25 \cdot 5^{x},-20 \cdot 2^{x}>-20 \cdot 5^{x} \Leftrightarrow \\
& \Leftrightarrow\left(\frac{2}{5}\right)^{x}<1
\end{aligned}
$$

Answer: $\quad x \in(0 ; \infty)$.