Defining the DT LTI system
$ x[n] \rightarrow system \rightarrow y[n] = 5x[n] $
a) Finding the unit impulse response h[n] and the system function H(z).
$ x[n] = \delta [n] \rightarrow system \rightarrow y[n]=5\delta [n] $
Therefore the unit impulse response, $ h[n] = 5\delta [n] $
