Let p be a prime≡l (mod 5). If 2 is a quintic nonresidue (mod p) then 2p-1/5 ≡ α (mod p) for some fifth root of unity α5 (≢ 1) (mod p). Emma Lehmer has given an explicit expression for a5 in terms of a particular solution of a certain quadratic partition of p. In this paper we show how in principle the corresponding result can be obtained for any quintic nonresidue D(mod p). Full details are given for D=2, 3, 5.