Answer
$0.20$
Work Step by Step
Let $\theta = \csc^{-1} {5}$
Then, $\csc{\theta} = 5$.
Since $\sin{\theta}= \dfrac{1}{\csc{\theta}}$, then
$\sin{\theta} = \dfrac{1}{5}$
Thus,
$\theta = \sin^{-1} {\left(\frac{1}{5}\right)}\approx 0.20$
Therefore,
$\csc^{-1} {5} = \sin^{-1} {\left(\frac{1}{5}\right)} \approx \boxed{0.20}$