Advanced Air Mobility (AAM) is a promising field of services based on Unmanned Aerial Vehicles (UAVs), which aims to provide people and cargo transportation services in underserved areas. The recent advancements in the fields of aviation and mobile telecommunication networks have opened up multiple opportunities for the development of disruptive AAM applications. This paper presents the overview and identifies the major requirements of emerging AAM use cases to confront them with the features provided by the 5G System (5GS), which is commonly considered the key enabler in providing commercial AAM services. The major benefits, gaps, and issues regarding using 5GS to serve AAM operations are identified and discussed. Finally, the future perspectives for AAM services are outlined with a focus on the potential benefit that can be provided as the mobile network evolves towards 6G.