x^{4} - 25
There is no greatest common factor here. Though, notice that it is the difference of two perfect squares.
x^{4} - 25 = ( x^{2} )^{2} - (5)^{2}
Thus, we can employ the third special form from above.
x^{4} - 25 =( x^{2 }+ 5)(x^{2 }- 5)