  This paper reports on our study of the edge of the 2/5 fractional quantum
Hall state, which is more complicated than the edge of the 1/3 state because of
the presence of a continuum of quasi-degenerate edge sectors corresponding to
different partitions of composite fermions in the lowest two {\Lambda} levels.
The addition of an electron at the edge is a non-perturbative process and it is
not a priori obvious in what manner the added electron distributes itself over
these sectors. We show, from a microscopic calculation, that when an electron
is added at the edge of the ground state in the [N_1, N_2] sector, where N_1
and N_2 are the numbers of composite fermions in the lowest two {\Lambda}
levels, the resulting state lies in either [N_1 + 1, N_2] or [N_1, N_2 + 1]
sector; adding an electron at the edge is thus equivalent to adding a composite
fermion at the edge. The coupling to other sectors of the form [N_1 + 1 + k,
N_2 - k], k integer, is negligible in the asymptotically low-energy limit. This
study also allows a detailed and substantial comparison with the two-boson
model of the 2/5 edge. We compute the spectral weights and find that while the
individual spectral weights are complicated and non-universal, their sum is
consistent with an effective two-boson description of the 2/5 edge.
