Answer
$6x^3y^2\sqrt[]{xy}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\sqrt[]{4x^7y^5}+9x^2\sqrt[]{x^3y^5}-5xy\sqrt[]{x^5y^3}
\\=
\sqrt[]{4x^6y^4\cdot xy}+9x^2\sqrt[]{x^2y^4\cdot xy}-5xy\sqrt[]{x^4y^2\cdot xy}
\\=
2x^3y^2\sqrt[]{xy}+9x^2\cdot xy^2\sqrt[]{xy}-5xy\cdot x^2y\sqrt[]{xy}
\\=
2x^3y^2\sqrt[]{xy}+9x^3y^2\sqrt[]{xy}-5x^3y^2\sqrt[]{xy}
\\=
6x^3y^2\sqrt[]{xy}
.\end{array}
