When we simplify radicals in a fraction, we have to rationalize the denominator where the radical is at.
There is a rule that shows (a-b)(a+b)=a^2-b^2.
So in the fraction, 5/(sqrt3 - 2) , the denominator (sqrt3-2) represents (a-b) in the rule of (a-b)(a+b)=a^2-b^2. To get rid of a surd, we can square the surd as seen in a^2-b^2
Let's place sqrt3 as a and 2 as b.
Hence, (sqrt3-2)(sqrt3+2) = (sqrt3)^2- 2^2
As we remember, the square of a radical/surd rationalises the radical.
(sqrt3)^2= 3
So what we can do is to muiltiply 5/(sqrt3 - 2) x (sqrt3+2)/(sqrt3 + 2) where (sqrt3+2)/(sqrt3 + 2)= 1 so it does not make a difference to the value of the product.
(5(sqrt3+2))/((sqrt3 - 2)(sqrt3+2)=(5sqrt3+10)/((sqrt3)^2-2^2)=(5sqrt3+10)/(3-4)=(5sqrt3+10)/(-1)= -5sqrt3-10
5/(sqrt3 - 2)= -5sqrt3-10 =-18.66 (2 d.p.)
