The dynamic nature of wireless links and the mobility of devices connected to the Internet of Things (IoT) over fifth-generation (5G) networks (IoT-5G), on the one hand, empowers pervasive healthcare applications. On the other hand, it allows eavesdroppers and other illegitimate actors to access secret information. Due to the poor time efficiency and high computational complexity of conventional cryptographic methods and the heterogeneous technologies used, it is easy to compromise the authentication of lightweight wearable and healthcare devices. Therefore, intelligent authentication, which relies on artificial intelligence (AI), and sufficient network resources are extremely important for securing healthcare devices connected to IoT-5G. This survey considers intelligent authentication and includes a comprehensive overview of intelligent authentication mechanisms for securing IoT-5G devices deployed in the healthcare domain. First, it presents a detailed, thoughtful, and state-of-the-art review of IoT-5G, healthcare technologies, tools, applications, research trends, challenges, opportunities, and solutions. We selected 20 technical articles from those surveyed based on their strong overlaps with IoT, 5G, healthcare, device authentication, and AI. Second, IoT-5G device authentication, radio-frequency fingerprinting, and mutual authentication are reviewed, characterized, clustered, and classified. Third, the review envisions that AI can be used to integrate the attributes of the physical layer and 5G networks to empower intelligent healthcare devices. Moreover, methods for developing intelligent authentication models using AI are presented. Finally, the future outlook and recommendations are introduced for IoT-5G healthcare applications, and recommendations for further research are presented as well. The remarkable contributions and relevance of this survey may assist the research community in understanding the research gaps and the research opportunities relating to the intelligent authentication of IoT-5G healthcare devices.