  We present the result of our spectroscopic follow-up observation for faint
quasar candidates at z~5 in a part of the Canada-France-Hawaii Telescope Legacy
Survey wide field. We select nine photometric candidates and identify three z~5
faint quasars, one z~4 faint quasar, and a late-type star. Since two faint
quasar spectra show Civ emission line without suffering from a heavy
atmospheric absorption, we estimate the black hole mass (M$_{BH}$) and
Eddington ratio (L/L$_{Edd}$) of them. The inferred log M$_{BH}$ are
9.04+/-0.14 and 8.53+/-0.20, respectively. In addition, the inferred log
(L/L$_{Edd}$) are -1.00+/-0.15 and -0.42+/-0.22, respectively. If we adopt that
L/L$_{Edd}$= constant or $\propto$ (1+z)^2, the seed black hole masses
(M$_{seed}$) of our z~5 faint quasars are expected to be >10^5 M$_\odot$ in
most cases. We also compare the observational results with a mass accretion
model where angular momentum is lost due to supernova explosions (Kawakatu &
Wada 2008). Accordingly, M$_{BH}$ of the z~5 faint quasars in our sample can be
explained even if M$_{seed}$ is ~10^3M$_\odot$. Since z~6 luminous qusars and
our z~5 faint quasars are not on the same evolutionary track, z~6 luminous
quasars and our z~5 quasars are not the same populations but different
populations, due to the difference of a period of the mass supply from host
galaxies. Furthermore, we confirm that one can explain M$_{BH}$ of z~6 luminous
quasars and our z~5 faint quasars even if their seed black holes of them are
formed at z~7.
