$5\sqrt{a}+6\sqrt{\dfrac{a}{4}}-a\sqrt{\dfrac{4}{a}}+\sqrt{5}$
$5\sqrt{a}+\dfrac{6\sqrt{a}}{2}-\dfrac{2a}{\sqrt{a}}+\sqrt{5}$
$5\sqrt{a}+\dfrac{3.2.\sqrt{a}}{2}-\dfrac{2.\sqrt{a}.\sqrt{a}}{\sqrt{a}}+\sqrt{5}$
$=5\sqrt{a}+3\sqrt{a}-2\sqrt{a}+\sqrt{5}$
$=6\sqrt{a}+\sqrt{5}$