Matlab filter implementation
Your filter is a 5-tap delay line FIR filter. The FIR filter's coefficients are [2 6 1 5 1]. If x is your filter's input sequence and you execute the following MATLAB command:
h = [2 6 1 5 1];

you can then implement the filter (to produce a y output sequence) using the following MATLAB command:
y = filter(h, 1, x);

You can see your filter's frequency magnitude and phase responses by executing the following MATLAB command:
freqz(h, 1, 256)