Reconfigurable intelligent surface (RIS) with 1-bit phase resolution suffers from high side lobe levels (SLLs) in the near field and pronounced quantization lobe levels (QLLs) in the far field, which is detrimental for the quality of wireless communication. RIS design is further challenging in the mm-wave bands, where typically large bandwidths are required. To address these limitations, this work proposes a novel wideband 5G mm-Wave RIS with 2-bit phase quantization, capable of covering the entire 5G n258 band. The proposed unit cell design is a combination of a grounded main slot, a parasitic slot, and a coupling patch, utilizing only two PIN diodes. This design achieves a 2-bit bandwidth (BW) of 24.1--27.7 GHz (13.9\%) and an effective 1-bit BW of 20.0--28.9 GHz (36.4\%). The unit cell features a compact size of 0.39$λ$ $\times$ 0.39$λ$, providing decent angular stability of $\pm30^\circ$ as well as eliminating the grating lobes. Based on this unit cell design, a 20 $\times$ 20 RIS array has been designed, fabricated, and experimentally characterized. The measured results demonstrate that, within the 5G n258 band, the proposed 2-bit 5G mm-Wave RIS achieves an SLL of -15.4 dB in the near field, representing a 7.6 dB improvement compared to its 1-bit counterpart. Furthermore, it has almost negligible QLL (-14.6 dB) in the far field, providing a suppression of 13.3 dB relative to the 1-bit design. Thus, the proposed 2-bit mm-Wave RIS offers wideband performance, low SLL, negligible QLL, decent angular stability, and a broad beam scanning range of 50$^\circ$, making it a promising solution for high-resolution and low-interference mm-Wave wireless communication systems.