Low-luminosity quasars at z ~ 5 are key ingredients to construct a reliable faint end of the quasar luminosity function. In our work, we tried to make a novel quasar selction consisting of an artificial neural network and Bayesian statistics to find the faintest quasars reaching M_{1450} ~ -22 mag, which is ~ 1 mag deeper than previous surveys. Using quasar SED models and a source catalog from the deep layer of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP), we prepared training samples for quasar at z=4.5-5.5 and non-quasar classes, respectively. An artificial neural network determines whether an object is a quasar or not using multi-dimensional decision boundaries in color spaces. Bayesian information criterion indicates promising candidates by comparing quasar and star best-fit SED models. The combination of artificial neural network and Bayesian statistics utilizes all the flux measurements, enabling us to maximize the chance for finding high-redshift quasars as well as minimize the probability of containing contamination sources in our final candidates. As a result, we could build the quasar luminosity function with the most reliable faint-end slope of -1.6, which is a mid-value of previously reported slopes from -2.0 to -1.2.