The domain of $sec5x$ is 

The given function is $f\left(x\right)=sec5x$

Secx is not defined at multiples of $\frac{\pi }{2}$

Hence, $sec5x$ is not defined at odd multiples of $\frac{\pi }{10}$

Therefore, the domain of the function $f\left(x\right)=sec5x$ is $\boxed{R-\left\{\frac{\left(2n+1\right)\pi }{10};n\in Z\right\}}$