7.038. $\lg \left(625 \sqrt[5]{5^{x^{2}-20 x+55}}\right)=0$.

7.038. $\lg \left(625 \sqrt[5]{5^{x^{2}-20 x+55}}\right)=0$.
## Solution.

From the condition, we have $625 \cdot 5^{\frac{x^{2}-20 x+55}{5}}=1.5^{\frac{x^{2}-20 x+55}{5}}=5^{-4}$, from which $\frac{x^{2}-20 x+55}{5}=-4, x^{2}-20 x+75=0$. Then $x_{1}=5 ; x_{2}=15$.

Answer: $5 ; 15$.