Factorize each of the following algebraic expression:

$a^{2}-8 a b+16 b^{2}-25 c^{2}$

$=\left(a^{2}-8 a b+16 b^{2}\right)-25 c^{2}$

$=\left[a^{2}-2 \times a \times 4 b+(4 b)^{2}\right]-25 c^{2}$

$=(a-4 b)^{2}-(5 c)^{2}$

$=[(a-4 b)-5 c][(a-4 b)+5 c]$

$=(a-4 b-5 c)(a-4 b+5 c)$