The quasar luminosity function (QLF) provides us a clue to understand the evolution of supermassive black holes (SMBHs). Recent studies have derived QLFs at various redshifts over a wide luminosity range. They have suggested that the redshift evolution of the quasar number density is luminosity-dependent, in the sense that more luminous quasars show the peak of the number density at higher redshift (quasar down-sizing). However, this trend could be inverted (quasar up-sizing) at z~5 as suggested from deep X-ray observations, though it is totally unclear due to insufficient area and sensitivity in past surveys. To reveal the evolution of SMBHs, measuring the QLF for a faint side at z~5 is essential. Therefore we are trying to search for low-luminosity quasars at z~5 with using the WIDE survey data in a part of the Subaru strategic program (SSP) with Hyper Suprime-Cam (HSC). This survey covers a wide survey area (~200 deg2) and has deep sensitivity (i_lim~26) enough to observe faint quasars at z~5. We selected candidates of low-luminosity quasars at z~5 by adopting the so-called Lyman-break method. As the result, we obtained a large sample of quasar candidates at z~5 with a luminosity range of -26.5 < M_1450 < -22.5. This luminosity range is about 1 mag deeper than SDSS Stripe 82. Furthermore we conducted the spectroscopic observation for our candidates with Cerro Tololo Inter-American Observatory / the 4m Blanco telescope. In this presentation, I would like to show the details of our photometric and spectroscopic analysis, and discuss the cosmological evolution of SMBHs.