smc

By the change-of-base formula, we can simplify the left side of the equation: $({\log }_{3}x)({\log }_{x}5)=(\frac{{\log }_x}{{\log }_3})(\frac{{\log }_5}{{\log }_x})=\frac{{\log }_5}{{\log }_3}$. We see that this in fact simplifies to ${\log }_{3}5$, which will always equal the right side of the equation, since they are the same exact expressions. But we have to be careful because $x\ne 1$. Plugging in $x=1$, the left side would equal $({\log }_{3}1)({\log }_{x}5)=0\cdot {\log }_{x}5=0$, and ${\log }_{3}5$ definitely does not equal $0$. Besides $1$, $x$ can take on any positive value, and the equation would work. Therefore, the answer is $\boxed{\text{all positive }x\ne 1}$