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To investigate [sup 5]H resonance states with a better instrumental resolution, we utilized the two-neutron transfer reaction [sup 3]H(t,p)[sup 5]H 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 θ[sub lab]=18[sup °]–32[sup °] in ptn coincidence events was attributed to the states of the [sup 5]H nucleus. Two resonance states situated at 1.8±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 [sup 5]H nucleus. The peak located close to E[sub [sup 5]H]=1.8 MeV was clearly seen in the [sup 5]H spectrum obtained from the energy distributions of [sup 3]H nuclei emitted in the reaction [sup 2]H([sup 6]He, [sup 5]H)[sup 3]He at θ[sub lab]=17[sup °]–32[sup °]. The width (Γ[sub obs]≤0.5 MeV) obtained for the two [sup 5]H resonance states is surprisingly small. A state of [sup 4]H with E[sub res]=3.3 MeV and γ[sup 2]=2.3 MeV was obtained in the reaction [sup 2]H(t, p)[sup 4]H from the spectra of protons leaving the target at θ[sub lab]=18[sup °]–32[sup °] and detected in coincidence with neutrons emitted in the decay of [sup 4]H nuclei.© 2003 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]