Launched in 2017, FORMOSAT-5 is a spacecraft located on a 720 km Sun synchronous orbit carrying indigenously developed payloads for Earth observation and in-situ ionospheric measurements. The FORMOSAT-5 attitude and orbit control subsystem (AOCS) contains a navigation filter utilizing a numerical orbit propagator to provide estimates of spacecraft inertial position and velocity when the onboard GPS receiver is not available. Times during which the onboard GPS is available provide a unique opportunity to assess the performance of the orbit propagator, as well as to explore further improvements. In this paper, we report the variation of the FORMOSAT-5 orbit propagation error during different seasons, as well as geomagnetic and solar activity conditions. The effects on orbit propagation error by introducing drag effects from various empirical thermospheric models is also explored. The results will be used to improve navigation and tracking functions for future Taiwanese satellites, including those of the six FORMOSAT-7/COSMIC-2 satellites, which will be located at lower orbits subject to increased perturbation from drag. The results also provide insight into the neutral density modeling capability of current empirical thermosphere models, which are also a key tool for understanding thermosphere and ionosphere variability.