Answer
$-5 - \frac{5}{2}\sqrt{6}$
Work Step by Step
Rationalize the denominator by multiplying $2+\sqrt{6}$ to both the numerator and the denominator to have:
$=\dfrac{5}{2-\sqrt{6}} \cdot \dfrac{2+\sqrt{6}}{2+\sqrt{6}}
\\=\dfrac{10+5\sqrt{6}}{4-6}
\\=\dfrac{10+5\sqrt{6}}{-2}
\\=-5 - \frac{5}{2}\sqrt{6}$
