Spectrum sharing enables access to additional bandwidth for 5G networks but also introduces intermittency due to hierarchical access and incumbent protection. When a shared band becomes unavailable, a base station operating solely on that band may be forced to vacate the spectrum, triggering a massive handover if a large number of user equipments (UEs) are involved. In this paper, we study the performance of the 5G contention-based random access channel (RACH) procedure under such massive handover events. We develop an analytical model to characterize the random access completion time, defined as the time required for all UEs to successfully complete the RACH process. We first analyze the performance of the uniform random backoff specified in the current 3GPP standards and demonstrate its limitations under bursty access. We then design two dynamic backoff schemes with dedicated backoff distributions that improve RACH efficiency compared to uniform backoff. Finally, we study the structure of the optimal backoff strategy in an idealized setting and show that the proposed designs achieve performance close to the theoretical optimum. These results provide insights into RACH design for spectrum-sharing networks and suggest potential directions for future standardization.