Outage event caused by dynamic link blockage at millimeter-wave (mmWave) frequencies is a challenging problem for cell-edge users. To address it, 3GPP is currently working on multi-connectivity mechanisms that allow a user to remain connected to several mmWave access points simultaneously, as well as switch between them in case its active connection drops. However, the actual number of such simultaneous links-named the degree of multi-connectivity-to reach the desired tradeoff between the system design simplicity and the outage probability levels remains an open research question. In this work, we characterize the outage probability and spectral efficiency associated with different degrees of multi-connectivity in a typical 5G urban scenario, where the line-of-sight propagation path can be blocked by buildings as well as humans. These results demonstrate that the degrees of multi-connectivity of up to 4 offer higher relative gains. Our analytical framework can be further employed for the performance analysis of multi-connectivity-capable mmWave systems across their different deployment configurations.