Answer
$-5\sqrt{2}$
Work Step by Step
Extracting the factor that is a perfect power of the index, then
\begin{array}{l}\require{cancel}
5\sqrt{8}-3\sqrt{50}
\\\\=
5\sqrt{4\cdot2}-3\sqrt{25\cdot2}
\\\\=
5\sqrt{(2)^2\cdot2}-3\sqrt{(5)^2\cdot2}
\\\\=
5(2)\sqrt{2}-3(5)\sqrt{2}
\\\\=
10\sqrt{2}-15\sqrt{2}
.\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
10\sqrt{2}-15\sqrt{2}
\\\\=
(10-15)\sqrt{2}
\\\\=
-5\sqrt{2}
.\end{array}
