#### Answer

$x\approx0.050$

#### Work Step by Step

In exponential form, the given logarithmic equation, $
5\ln x=-15
,$ is equivalent to
\begin{array}{l}\require{cancel}
\ln x=-\dfrac{15}{5}
\\\\
\ln x=-3
\\\\
\log_e x=-3
\\\\
x=e^{-3}
.\end{array}
Hence, the value of the variable that satisfies the given equation is
\begin{array}{l}\require{cancel}
x\approx0.050
.\end{array}