$ \,\ x[n] = 5*u[n-5] + 6*u[n+6] $
We obtain $ h[n] $ by finding the response of $ x[n] $ to the unit impulse response ($ \delta[n] $).
$ \,\ h[n] = 5*\delta[n-5] + 6*\delta[n+6] $
$ \,\ H[z] = $
