$$\frac{2\sqrt{45}+\sqrt{90}+5\sqrt5}{\sqrt{15}}\\\\
=\frac{2\sqrt{9*5}+\sqrt{9*5*2}+5\sqrt5}{\sqrt{3*5}}\\\\
=\frac{2\sqrt{9}\sqrt5+\sqrt{9}\sqrt5 \sqrt2 +5\sqrt5}{\sqrt{3}\sqrt5}\\\\
=\frac{6\sqrt5+3\sqrt5 \sqrt2 +5\sqrt5}{\sqrt{3}\sqrt5)}\\\\
=\frac{\sqrt5(6+3 \sqrt2 +5)}{\sqrt3\sqrt5}\\\\
=\frac{(11+3 \sqrt2)}{\sqrt3}\\\\
=\frac{(11+3 \sqrt2)\sqrt3}{\sqrt3 \sqrt3}\\\\
=\frac{11\sqrt3 +3 \sqrt6}{3}\\\\$$

.