$(x^2+4y^2-5)^2-16(x^2y^2-2xy+1)$
$=(x^2+4y^2-5)^2-4^2(xy-1)^2$
$=(x^2+4y^2-5)^2-[4(xy-1)]^2$
$=(x^2+4y^2-5)^2-(4xy-4)^2$
$=(x^2+4y^2-5+4xy-4)(x^2+4y^2-5-4xy+4)$
$=[(x^2+4xy+4y^2)-(5+4)][(x^2-4xy+4y^2)-(5-4)]$
$=[(x+2y)^2-9][(x-2y)^2-1]$
$=[(x+2y)^2-3^2][(x-2y)^2-1^2]$
$=(x+2y+3)(x+2y-3)(x-2y+1)(x-2y-1)$