[tex]\Big|5- \sqrt{5} \Big|+\Big|2- \sqrt{3} \Big|-2 \\ \\
5 \ \textgreater \ \sqrt{5}~~\Longrightarrow~~\Big|5- \sqrt{5}\Big|=5 - \sqrt{5} \\ \\
2 \ \textgreater \ \sqrt{3}~~\Longrightarrow~~ \Big|2\ \textgreater \ \sqrt{3}\Big|= 2 - \sqrt{3} \\ \\
\Longrightarrow~~\Big|5- \sqrt{5} \Big|+\Big|2- \sqrt{3} \Big|-2= 5 - \sqrt{5}+2 - \sqrt{3}-2=\boxed{5-\sqrt{5}-\sqrt{3}}[/tex]
