Let $x_1=\sqrt{10}$ and $y_1=\sqrt3$.  For all $n\geq 2$, let \begin{align*}x_n&=x_{n-1}\sqrt{77}+15y_{n-1}\\y_n&=5x_{n-1}+y_{n-1}\sqrt{77}\end{align*} Find $x_5^6+2x_5^4-9x_5^4y_5^2-12x_5^2y_5^2+27x_5^2y_5^4+18y_5^4-27y_5^6.$

Let's think step by step and output the final answer within \boxed{}.
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