Ensuring the security of vertical applications in fifth-generation (5G) mobile communication systems and previous generations is crucial. These systems must prioritize maintaining the confidentiality, integrity, and availability of services and data. Examples of vertical applications include smart cities, smart transportation, public services, Industry 4.0, smart grids, smart health, and smart agriculture. Each vertical application has specific security requirements and faces unique threats within the mobile network environment. Thus, it is essential to implement comprehensive and robust security measures. This approach helps minimize the attack surface and effectively manage risks. This survey thoroughly examines mobile networks and their security challenges in vertical applications, shedding light on associated threats and potential solutions. Our study considers the interplay between security considerations in 5G, legacy networks, and vertical applications. We emphasize the challenges, opportunities, and promising directions for future research in this field and the importance of securing vertical applications in the evolving landscape of mobile technology.