$f(x)=\frac{1-4x}{1+4x}=\frac{2}{1+4x}-\frac{1+4x}{1+4x}=\frac{2}{1+4x}-1$ $\Rightarrow f'''(x)=-\frac{2\cdot 4^3 \cdot 2 \cdot 3}{(1+4x)^4}=-\frac{768}{(1+4x)^4}$ and replace with $x=5$.