This paper proposes a cellular network exploiting millimeter-wave (mmWave) and ultra-densified base stations (BSs) to achieve the far-reaching 5G aim in downlink average rate. The mmWave overlaid network however incurs a pitfall that its ample data rate is only applicable for downlink transmissions due to the implementation difficulty at mobile users, leading to an immense difference between uplink and downlink rates. We therefore turn our attention not only to maximize downlink rate but also to ensure the minimum uplink rate. With this end, we firstly derive the mmWave overlaid ultra-dense cellular network spectral efficiencies for both uplink and downlink cases in closed forms by using stochastic geometry via a lower bound approximation. In a practical scenario, such tractable results of the proposed network reveal that incumbent micro-wave ($μ$Wave) cellular resource should be mostly dedicated to uplink transmissions in order to correspond with the mmWave downlink rate improvement. Furthermore, increasing uplink rate via $μ$Wave BS densification cannot solely cope with the mmWave downlink/uplink rate asymmetry, and thus requires additional $μ$Wave spectrum in 5G cellular networks.