Factorize each of the following expression:

$x^{4}-625$

$=\left(x^{2}\right)^{2}-25^{2}$

$=\left(x^{2}+25\right)\left(x^{2}-25\right)$

$=\left(x^{2}+25\right)\left(x^{2}-5^{2}\right)$

$=\left(x^{2}+25\right)(x+5)(x-5)$