\[\begin{array}{l}
{\left( {{x^2} + {y^2} - 5} \right)^2} - 4{x^2}{y^2} - 16xy - 16\\
= {\left( {{x^2} + {y^2} - 5} \right)^2} - \left( {4{x^2}{y^2} + 16xy + 16} \right)\\
= {\left( {{x^2} + {y^2} - 5} \right)^2} - {\left( {2xy + 4} \right)^2}\\
= \left( {{x^2} + {y^2} - 5 - 2xy - 4} \right)\left( {{x^2} + {y^2} - 5 + 2xy + 4} \right)\\
= \left[ {{{\left( {x - y} \right)}^2} - 9} \right]\left[ {{{\left( {x + y} \right)}^2} - 1} \right]\\
= \left( {x - y - 3} \right)\left( {x - y + 3} \right)\left( {x + y - 1} \right)\left( {x + y + 1} \right).
\end{array}\]
