Do you mean z5=1, which has 5 zeroes or roots.
z5-1=(z-1)(z4+z3+z2+z+1)=0, so z=1 is the only real root.
De Moivre: einθ=cos(nθ)+isin(nθ)=(cosθ+isinθ)5.
z5=eiθ=1=cos(2πm)+isin(2θm), where m is an integer, 0≤m<5
z=eiθ/5=cos(⅖πm)+isin(⅖πm). The 5 roots correspond to the vertices of a regular pentagon of radius 1.
The roots are found by plugging in the values of m.
When m=0 z=1 (the real root). When m=1, z=cos(⅖π)+isin(⅖π).
The roots correspond to the polar coordinates (1,0), (1,⅖π), (1,⅘π), (1,1⅕π), (1,1⅗π), which are the vertices of the pentagon.