I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal. So, I am clueless!
#Fourier #transform #question #discrete
Have you tried just finding $$ Y(e^\omega) $$ symbolically, and then solving? For $$ \omega \in \left \lbrace 2 \pi k / 5 \right \rbrace $$ there should only be ten equations in ten unknowns.