The expected fifth generation (5G) networks allow for highly accurate direction of arrival and time of arrival (ToA) estimation, thus providing a convenient environment for device positioning, if designed properly. However, utilizing ToA measurements for positioning requires a tight synchronization not only between the target devices but also among the network elements. In this paper, we propose a joint positioning and synchronization solution building on the premises of the envisioned cmWave-based 5G ultra-dense networks and time-varying clock models. In addition to device location estimates, also relative clock offsets and skews are estimated and tracked within the proposed extended Kalman filter based solutions, which can be further used by a network operator in synchronizing the active network elements and devices within the network. Based on extensive simulations and numerical evaluations, accurate positioning performance can be achieved while tracking the clock parameters under time-varying clock errors.