\[1 - x^{2} + 10xy - 25y^{2} =\]
\[= 1 - \left( x^{2} - 10xy + 25y^{2} \right) = 1^{2} - (x - 5y)^{2} =\]
\[= (1 - x + 5y)(1 + x - 5y)\]