We know the n>1-th roots of unity that are of the form e^{m*pi*i/n} where m is a positive integer and gcd(m,n)=1 will be a generator for the group of all roots of unity.

Since 5 is a prime there are exactly 4 primitive roots of unities (because those the ones that form generators):

e^{pi*i/5},e^{2pi*i/5},e^{3pi*i/6},e^{4pi*i/5}