Answer
$2(x^{2}+4)^{4}(x-2)^{3}(7x^{2}-10x+8)$
Work Step by Step
Factor out $x^2+4$ and $x-2$:
$5(x^{2}+4)^{4}(2x)(x-2)^{4}+(x^{2}+4)^{5}(4)(x-2)^{3}=2(x^{2}+4)^{4}(x-2)^{3}[(5)(x)(x-2)+(x^{2}+4)(2)]
=2(x^{2}+4)^{4}(x-2)^{3}(5x^{2}-10x+2x^{2}+8)=2(x^{2}+4)^{4}(x-2)^{3}(7x^{2}-10x+8)$
