Answer
$\frac{\sqrt3-1}{2\sqrt2}$
Work Step by Step
Using the given formula and the known values: $\cos(-\frac{5\pi}{12})=\cos(-\pi/6)\cos(-\pi/4)-\sin(-\pi/6)\sin(-\pi/4)=\frac{\sqrt3}{2}\frac{1}{\sqrt2}-\frac{1}{2}\frac{1}{\sqrt2}=\frac{\sqrt3-1}{2\sqrt2}$
