Answer
$x^{10}-8x^5+16$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
(x^5-4)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(x^5)^2+2(x^5)(-4)+(-4)^2
\\\\=
x^{10}-8x^5+16
.\end{array}