Answer
$x=\dfrac{5}{2}$
Work Step by Step
Using the properties of logarithms and since $\log_b x=y$ is equivalent to $b^y=x$, then,
\begin{array}{l}
\log_5 x+\log_5 10=2\\\\
\log_5 x(10)=2\\\\
\log_5 10x=2\\\\
10x=5^2\\\\
10x=25\\\\
x=\dfrac{25}{10}\\\\
x=\dfrac{5}{2}
.\end{array}
