$\lim _{h \rightarrow 0} \frac{\cos \left(\frac{\pi}{5}+h\right)-\cos \left(\frac{\pi}{5}\right)}{h}$ is

Step 1 ：Given the limit problem: \(\lim _{h \rightarrow 0} \frac{\cos \left(\frac{\pi}{5}+h\right)-\cos \left(\frac{\pi}{5}\right)}{h}\)

Step 2 ：This is a common calculus problem and the function in question is a difference quotient, which is used to find the derivative of a function.

Step 3 ：The derivative of \(\cos(x)\) is \(-\sin(x)\), so we can use this fact to find the limit.

Step 4 ：Let's denote \(h = h\) and \(f = \left(\cos(h + \pi/5) - \sqrt{5}/4 - 1/4\right)/h\)

Step 5 ：By calculating the limit, we find that the limit of the function as \(h\) approaches 0 is \(-\sqrt{10 - 2\sqrt{5}}/4\). This is the derivative of the function at the point \(\pi/5\).

Step 6 ：Final Answer: \(\boxed{-\frac{\sqrt{10 - 2\sqrt{5}}}{4}}\)