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.
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