Time synchronization is one of the main building blocks for IEEE 802.1 Time Sensitive Network (TSN) based time aware industrial networks. 3rd generation partnership project (3GPP) has proposed new mechanisms in Release 16 in order for the 5G system (5GS) to interwork with Time Sensitive Networks (TSN). In this context, 3GPP has modelled the 5GS as IEEE 802.1AS time aware system in an integrated 5G-TSN network. The most demanding time synchronization error budget applicable to a 5GS (i.e., the 5G system end-to-end time error budget) used within the context of an integrated 5G-TSN network can be as lows as 900ns. Within the 5GS the radio link between a base station and user equipment (UE) is subject to propagation delay and the uncertainty associated with its estimation is considered to have a major contribution towards the 5GS error budget. This paper presents an end-to-end (E2E) analysis on the time synchronization solutions offered by the 5GS in the context of an integrated 5G-TSN network. Furthermore, the paper provides an in-depth analytical evaluation of propagation delay errors introduced based on two different propagation delay estimation methods.