Let x_{1}=\sqrt{10} and y_{1}=\sqrt{3}. For all n \geq 2, let
x_{n}=x_{n-1} \sqrt{77}+15 y_{n-1} \tag{A.4}
y_{n}=5 x_{n-1}+y_{n-1} \sqrt{77}\tag{A.5}
Find x_{5}^{6}+2 x_{5}^{4}-9 x_{5}^{4} y_{5}^{2}-12 x_{5}^{2} y_{5}^{2}+27 x_{5}^{2} y_{5}^{4}+18 y_{5}^{4}-27 y_{5}^{6}.