Answer
$0$
Work Step by Step
We have:
$\cos\left(-\dfrac{5\pi}{4}\right)=-\cos \dfrac{\pi}{4}=-\dfrac{\sqrt 2}{2}$
(we used the reference angle $\dfrac{\pi}{4}$ and the sign minus because $-\dfrac{5\pi}{4}$ is in Quadrant II where cosine is negative.)
$\cos\dfrac{3\pi}{4}=-\cos \dfrac{\pi}{4}=-\dfrac{\sqrt 2}{2}$
(we used the reference angle $\dfrac{\pi}{4}$ and the sign minus because $\dfrac{3\pi}{4}$ is in Quadrant II)
Evaluate the given expression to obtain::
$\cos\left(-\dfrac{5\pi}{4}\right)-\cos\dfrac{3\pi}{4}=-\dfrac{\sqrt 2}{2}-\left(-\dfrac{\sqrt 2}{2}\right)=0$
