7.057. $5^{x+6}-3^{x+7}=43 \cdot 5^{x+4}-19 \cdot 3^{x+5}$.
Solution.

We have $5^{6} \cdot 5^{x}-43 \cdot 5^{4} \cdot 5^{x}=3^{7} \cdot 3^{x}-19 \cdot 3^{5} \cdot 3^{x},\left(\frac{5}{3}\right)^{x}=\left(\frac{5}{3}\right)^{-3}$, from which $x=-3$.

Answer: -3.