Version 5 (v05) of the thermospheric wind data from the Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI) instrument on the Ionospheric CONnections (ICON) mission has been recently released, which largely avoids local-time dependent artificial baseline drifts that are found in previous versions of the ICON/MIGHTI wind data. This paper describes monthly climatologies of zonal-mean winds and tides based on the v05 ICON/MIGHTI data under geomagnetically quiet conditions (Hp30 < 3o) during April 2020-March 2022. Green-line winds in the lower thermosphere (90-110 km) and red-line winds in the middle thermosphere (200-300 km) are analyzed, as these data cover both daytime and nighttime. The altitude and latitude structures of zonal-mean winds and tides are presented for each month, and the results are compared with the widely-used empirical model, Horizontal Wind Model 2014 (HWM14). The v05 wind retrieval algorithm does not involve HWM14. The ICON/MIGHTI and HWM14 results are in general agreement, providing a validation of the v05 ICON/MIGHTI data. The agreement is especially good for the zonal-mean winds. The tidal amplitudes in HWM14 are often too small compared with those from ICON/MIGHTI as well as previous studies. A more accurate description of tides in the thermosphere is key to the future improvement of HWM.