  The continuum resonance spectrum of $^5$H ($^3$H+$n$+$n$) is investigated by
use of the complex scaled hyperspherical adiabatic expansion method. The
crucial $^3$H-neutron potential is obtained by switching off the Coulomb part
from successful fits to $^3$He-proton experimental data. These two-body
potentials must be expressed exclusively by operators conserving the
nucleon-core mean field angular momentum quantum numbers. The energies $E_R$
and widths $\Gamma_R$ of the $1/2^+$ ground-state resonance and the lowest two
excited $5/2^+$ and $3/2^+$-resonances are found to be $(1.6,1.5)$ MeV,
$(2.8,2.5)$ MeV and $(3.2,3.9)$ MeV, respectively. These results agree with
most of the experimental data. The energy distributions of the fragments after
decay of the resonances are predicted.
