Rationalize the denominator:

$\dfrac{\sqrt{2}}{(\sqrt{2} + \sqrt{3} - \sqrt{5})}$.

Rationalizing the denomaintor,

$\Rightarrow \dfrac{\sqrt{2}}{(\sqrt{2} + \sqrt{3} - \sqrt{5})} \times \dfrac{(\sqrt{2} + \sqrt{3} + \sqrt{5})}{(\sqrt{2} + \sqrt{3} + \sqrt{5})} \\[1em] \Rightarrow \dfrac{ \sqrt{2} \times (\sqrt{2}+ \sqrt{3} + \sqrt{5})} {(\sqrt{2}+ \sqrt{3} - \sqrt{5}) \times (\sqrt{2} + \sqrt{3} + \sqrt{5})} \\[1em] \Rightarrow \dfrac{(2 + \sqrt{6} + \sqrt{10})} {(2 + \sqrt{6} + \sqrt{10} + \sqrt{6} + 3 + \sqrt{15} - \sqrt{10} - \sqrt{15} - 5)} \\[1em] \Rightarrow \dfrac{(2 + \sqrt{6} + \sqrt{10})} {(2\sqrt{6})}$

Rationalizing again,

$\Rightarrow \dfrac{(2 + \sqrt{6} + \sqrt{10})} {(2\sqrt{6})} \times \dfrac{\sqrt{6}}{\sqrt{6}} \\[1em] \Rightarrow \dfrac{(2 + \sqrt{6} + \sqrt{10}) \times \sqrt{6}} {(2\sqrt{6})\times \sqrt{6}} \\[1em] \Rightarrow \dfrac{(2\sqrt{6} + 6 + \sqrt{60})} {12} \\[1em] \Rightarrow \dfrac{(2\sqrt{6} + 6 + \sqrt{15 \times 4})}{12} \\[1em] \Rightarrow \dfrac{2\sqrt{6} + 6 + 2\sqrt{15}}{12} \\[1em] \Rightarrow \dfrac{2(\sqrt{6} + 3 + \sqrt{15})}{12} \\[1em] \Rightarrow \dfrac{(\sqrt{6} + 3 + \sqrt{15})}{6}.$

Hence, on rationalizing $\dfrac{(\sqrt{6} + 3 + \sqrt{15})}{6} = \dfrac{(\sqrt{6} + 3 + \sqrt{15})}{6}$.