\[x^{2} - 4x - 5 =\]
\[= x^{2} - 4x + 4 - 9 =\]
\[= (x - 2)^{2} - 9 =\]
\[= (x - 2 - 3)(x - 2 + 3) =\]
\[= (x - 5)(x + 1)\ \]