Answer
$6i\sqrt{2}-5i$
Work Step by Step
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ and $i=\sqrt{-1},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{-72}-\sqrt{-25}
\\\\=
\sqrt{-1}\cdot\sqrt{72}-\sqrt{-1}\cdot\sqrt{25}
\\\\=
i\sqrt{72}-i\sqrt{25}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
i\sqrt{72}-i\sqrt{25}
\\\\=
i\sqrt{36\cdot2}-i\sqrt{25}
\\\\=
i\sqrt{(6)^2\cdot2}-i\sqrt{(5)^2}
\\\\=
i\cdot6\sqrt{2}-i\cdot5
\\\\=
6i\sqrt{2}-5i
.\end{array}
