A new Taiwanese satellite, FORMOSAT-5 (FS-5), with a payload remote sensing instrument (RSI) was launched in August 2017 to continue the mission of its predecessor FORMOSAT-2 (FS-2). Similar to FS-2, the RSI provides 2-m resolution panchromatic and 4-m resolution multi-spectral images as the primary payload on FS-5. However, the radiometric properties of the optical sensor may vary, based on the environment and time after being launched into the space. Thus, maintaining the radiometric quality of FS-5 RSI imagery is essential and significant to scientific research and further applications. Therefore, the objective of this study aimed at the on-orbit absolute radiometric assessment and calibration of on-orbit FS-5 RSI observations. Two renowned approaches, vicarious calibrations and cross-calibrations, were conducted at two calibration sites that employ a stable atmosphere and high surface reflectance, namely, Alkali Lake and Railroad Valley Playa in North America. For cross-calibrations, the Landsat-8 Operational Land Imager (LS-8 OLI) was selected as the reference. A second simulation of the satellite signal in the solar spectrum (6S) radiative transfer model was performed to compute the surface reflectance, atmospheric effects, and path radiance for the radiometric intensity at the top of the atmosphere. Results of vicarious calibrations from 11 field experiments demonstrated high consistency with those of seven case examinations of cross-calibration in terms of physical gain in spectra, implying that the practicality of the proposed approaches is high. Moreover, the multi-temporal results illustrated that RSI decay in optical sensitivity was evident after launch. The variation in the calibration coefficient of each band showed no obvious consistency (6%-24%) in 2017, but it tended to be stable at the order of 3%-5% of variation in most spectral bands during 2018. The results strongly suggest that periodical calibration is required and essential for further scientific applications.