The increasing demand for 5G and future networks requires ultra-low latency, even lower than current 5G levels. Precision Time Protocol White Rabbit (PTP-WR) currently offers sub-nanosecond accuracy, making it the leading synchronization solution for 5G. However, emerging applications in Extended Reality (ER) demand precision beyond the sub-nanosecond range. Quantum synchronization promises much higher accuracy, potentially reaching picosecond (ps) or femtosecond (fs) levels. This could greatly reduce the Time Error Budget (TEB) in 5G networks, where classical systems experience timing errors around 1.5μs in Time Division Duplex (TDD), influenced by factors like clock drift, propagation delays, noise, and holdover. On the other hand, quantum synchronization has the potential to significantly reduce synchronization errors. However, while achieving high-precision synchronization at every node is ideal, deploying quantum synchronization across all nodes remains impractical due to its high implementation costs. Therefore, this paper focuses on assessing synchronization performance, where quantum synchronization is present on the Primary Reference Time Clock (PRTC) side, and we evaluate its impact on the TEB using a simulation-based approach. We calculate TEB by modeling key factors through Time Deviation (TDEV) and Maximum Time Interval Error (MTIE). Our results show that while quantum synchronization improves precision, existing infrastructure introduces noise that limits the achievable TEB reduction. By removing holdover and noise, the TEB can be reduced to 1.1 us.