1. $\arcsin (\sin \sqrt{3})-\arcsin (\cos 5)=$
1. $\frac{5 \pi}{2}-5-\sqrt{3}$.
$$
\begin{aligned}
\text { Original expression } & =\arcsin (\sin (\pi-\sqrt{3}))-\arcsin \left(\sin \left(-\frac{3 \pi}{2}+5\right)\right) \\
& =(\pi-\sqrt{3})-\left(5-\frac{3 \pi}{2}\right)=\frac{5 \pi}{2}-5-\sqrt{3} .
\end{aligned}
$$