jmc

First, we combine like terms in the expression: $$\begin{array}{rl}(15x^3+80x-5)& -(-4x^3+4x-5)\\ & =15x^3+80x-5+4x^3-4x+5\\ & =19x^3+76x.\end{array}$$We can factor out a $19x$ from the expression, to get $$19x^3+76x=\boxed{19x(x^2+4)}.$$