Use a sum or difference formula to find the exact value of the following.
\[
\cos \frac{5 \pi}{7} \cos \frac{5 \pi}{42}-\sin \frac{5 \pi}{7} \sin \frac{5 \pi}{42}
\]

Step 1 ：The given expression is in the form of the cosine of the sum of two angles. The formula for the cosine of the sum of two angles is given by: \(\cos(a + b) = \cos a \cos b - \sin a \sin b\)

Step 2 ：So, we can rewrite the given expression as the cosine of the sum of the two angles \(\frac{5 \pi}{7}\) and \(\frac{5 \pi}{42}\).

Step 3 ：Let's denote \(a = \frac{5\pi}{7}\) and \(b = \frac{5\pi}{42}\).

Step 4 ：The sum of the angles is \(a + b = \frac{5\pi}{6}\).

Step 5 ：Using the cosine function, we find that the cosine of the sum of the angles is \(\cos(\frac{5\pi}{6}) = -\frac{\sqrt{3}}{2}\).

Step 6 ：Final Answer: The exact value of the given expression is \(\boxed{-\frac{\sqrt{3}}{2}}\).