A spectroscopic study of population of the excited 3s₂-3s₅ states (in Paschen’s notation) of neon atoms of the 2p⁵5s configuration was carried out in a pulsed discharge helium plasma with a small admixture of neon (pressure 38.1 Torr, [He]/[Ne] ≌ 10⁵). Study the response of the spectral line intensities to pulsed heating of electron gas by an electric field in the late afterglow made it possible to determine the dependences of the partial rates of population of the 3s₂-3s₅ states on electron temperature T_e for kT_e = 0.03–0.40 eV. At temperatures of 0.03–0.20 eV, the 3s₂–3s₅ states are populated mainly due to dissociative recombination of HeNe⁺ ions and electrons with the temperature dependences of recombination fluxes close to T_e ^−1.2. At temperatures of 0.20–0.40 eV, the rate of population of the 3s₂–3s₅ states was observed to increase via two mechanisms. One of them is the electron-impact excitation He(2³S₁) + e + 0.8 eV → He(2¹S₀) + e followed by excitation transfer from He(2¹S₀) to neon atoms; the second mechanism is presumably the threshold process of dissociative recombination of Ne₂ ⁺ ions (v = 0) in the ground vibrational state with electrons.