Answer
$\displaystyle \frac{5(\sqrt{3}+1)}{2}$
Work Step by Step
Use $(a+b)(a-b)=a^{2}-b^{2}\quad$ when rationalizing.
$[(a+\sqrt{b})(a-\sqrt{b})=a^{2}-b]$
$\displaystyle \frac{5}{\sqrt{3}-1}\cdot\frac{\sqrt{3}+1}{\sqrt{3}+1}=\frac{5(\sqrt{3}+1)}{3-1}$
$=\displaystyle \frac{5(\sqrt{3}+1)}{2}$
