#### Answer

$x=e^2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
5\ln x=10
,$ convert it to exponential form.
$\bf{\text{Solution Details:}}$
Dividing both sides by $
5
,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\ln x=\dfrac{10}{5}
\\\\
\ln x=2
.\end{array}
Since $\ln x=\log_e x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log_e x=2
.\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is
\begin{array}{l}\require{cancel}
e^2=x
\\\\
x=e^2
.\end{array}