Find all values of the parameter y for which the following system has a solution

x_5 + x_2 = yx_1
x_1 + x_3 = yx_2
x_2 + x_4 = yx_3
x_3 + x_5 = yx_4
x_4 + x_1 = yx_5

For each value of y, find all the solutions.