If $$\sqrt x - \frac{1}{{\sqrt x }} = \sqrt 5 ,$$    then $${x^2} + \frac{1}{{{x^2}}}$$  is equal to:

$$\eqalign{ & \sqrt x - \frac{1}{{\sqrt x }} = \sqrt 5 \cr & {\text{Square both side}} \cr & x + \frac{1}{x} - 2.x.\frac{1}{x} = 5 \cr & x + \frac{1}{x} = 5 + 2 \cr & {\text{Square both side}} \cr & {x^2} + \frac{1}{{{x^2}}} + 2.x.\frac{1}{x} = 49 \cr & {x^2} + \frac{1}{{{x^2}}} = 47 \cr} $$