Obtain the input impulse response h[n] and the system function H(z) of your system
Defining a DT LTI:
$ y[n] = x[n+5] + x[n-3]\, $
So, we have the unit impulse response:
$ h[n] = \delta[n-5] + \delta[n-3]\, $
Then we find the frequency response:
$ F(z) = \sum^{\infty}_{m=-\infty} h[m+5]e^{jm\omega} + h[m-3]e^{jm\omega}\, $
find m value to make the value inside the bracket zero
m = -5 for the first set and 3 for the second set
$ F(z) = e^{-5j\omega} + e^{3j\omega} \, $
