Answer: Option C
$$\eqalign{
& x + y = \sqrt 3 \,.......{\text{(i)}} \cr
& x - y = \sqrt 2 \,.......(ii) \cr
& {\text{From equation (i) and (ii)}} \cr
& x = \frac{{\sqrt 3 + \sqrt 2 }}{2} \cr
& y = \frac{{\sqrt 3 - \sqrt 2 }}{2} \cr
& {\text{So, }}8xy\left( {{x^2} + {y^2}} \right) \cr
& = 8 \times \frac{{\sqrt 3 + \sqrt 2 }}{2} \times \frac{{\sqrt 3 - \sqrt 2 }}{2}\left[ {\frac{{{{\left( {\sqrt 3 + \sqrt 2 } \right)}^2}}}{4} + \frac{{{{\left( {\sqrt 3 - \sqrt 2 } \right)}^2}}}{4}} \right] \cr
& = 2\left( {3 - 2} \right)\left[ {\frac{{3 + 2 + 2\sqrt 6 + 3 + 2 - 2\sqrt 6 }}{4}} \right] \cr
& = 2 \times 1 \times \frac{{10}}{4} \cr
& = 5 \cr} $$