\(\dfrac{5+\sqrt{5}}{\sqrt{5}}\)
\(=\dfrac{\sqrt{5}\cdot\sqrt{5}+\sqrt{5}}{\sqrt{5}}\)
\(=\dfrac{\sqrt{5}\cdot\sqrt{5}+\sqrt{5}\cdot1}{\sqrt{5}}\)
\(=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}}\)
\(=\sqrt{5}+1\)
\(=\dfrac{\sqrt{5}\cdot\sqrt{5}+\sqrt{5}\cdot1}{\sqrt{5}}=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}}=\sqrt{5}+1\)