7.049. $\lg (5-x)-\frac{1}{3} \lg \left(35-x^{3}\right)=0$.
## Solution.

Domain of definition: $\left\{\begin{array}{l}5-x>0, \\ 35-x^{3}>0,\end{array}, x<\sqrt[3]{35}\right.$.

From the condition, we have $3 \lg (5-x)=\lg \left(35-x^{3}\right), \lg (5-x)^{3}=\lg \left(35-x^{3}\right)$, hence $(5-x)^{3}=35-x^{3}, x^{2}-5 x+6=0$. Therefore, $x_{1}=2, x_{2}=3$.

Answer: $2 ; 3$.