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You can simply ask for the roots of cyclotomic polynomials
sage: R.<c> = Zq(125, prec=20)
sage: cyclotomic_polynomial(4).roots(multiplicities=False, ring=R)
[2 + 5 + 2*5^2 + 5^3 + 3*5^4 + 4*5^5 + ... + 4*5^17 + 4*5^19 + O(5^20),
3 + 3*5 + 2*5^2 + 3*5^3 + 5^4 + 2*5^6 + ... + 2*5^16 + 4*5^18 + O(5^20)]
Sadly, the zeta method is not available to give you a single primitive n-th root
sage: R.zeta(4)
Traceback (most recent call last):
...
NotImplementedError:
