Résumé : To investigate 5H resonance states with a better instrumental resolution, we utilized the two-neutron transfer reaction 3H(t, p)5H accomplished with the use of a cryogenic liquid-tritium target and 57.5-MeV triton beam. As a result of this study, a valuable fraction of protons detected at θlab = 18°-32° in ptn coincidence events was attributed to the states of the 5H nucleus. Two resonance states situated at 1.8 plusmn; 0.1 and 2.7 ± 0.1 MeV above the t + n + n decay threshold were obtained in the missing mass energy spectrum of the 5H nucleus. The peak located close to E5H = 1.8 MeV was clearly seen in the H spectrum obtained from the energy distributions of 3H nuclei emitted in the reaction 2H(6He, 5H)3He at θ lab = 17°-32°. The width (Γobs ≤ 0.5 MeV) obtained for the two 5H resonance states is surprisingly small. A state of 4H with Eres = 3.3 MeV and γ2 = 2.3 MeV was obtained in the reaction 2H(t, p)4H from the spectra of protons leaving the target at θlab = 18°-32° and detected in coincidence with neutrons emitted in the decay of 4H nuclei. © 2003 MAIK "Nauka/Interperiodica".