The evolving fifth generation (5G) cellular wireless networks are envisioned to overcome the fundamental challenges of existing cellular networks, e.g., higher data rates, excellent endto- end performance and user-coverage in hot-spots and crowded areas with lower latency, energy consumption and cost per information transfer. To address these challenges, 5G systems will adopt a multi-tier architecture consisting of macrocells, different types of licensed small cells, relays, and device-to-device (D2D) networks to serve users with different quality-of-service (QoS) requirements in a spectrum and energy-efficient manner. Starting with the visions and requirements of 5G multi-tier networks, this article outlines the challenges of interference management (e.g., power control, cell association) in these networks with shared spectrum access (i.e., when the different network tiers share the same licensed spectrum). It is argued that the existing interference management schemes will not be able to address the interference management problem in prioritized 5G multitier networks where users in different tiers have different priorities for channel access. In this context, a survey and qualitative comparison of the existing cell association and power control schemes is provided to demonstrate their limitations for interference management in 5G networks. Open challenges are highlighted and guidelines are provided to modify the existing schemes in order to overcome these limitations and make them suitable for the emerging 5G systems.