In this work, we propose a novel approach combining 5G network slicing and nonorthogonal multiple access (NOMA) to transmit medical data in a mobile hospital system. We consider both the uplink and downlink of a 5G cellular network with an ambulance bus located at a remote site for data transmission in the uplink scenario and a hospital unit as the receiving site in the downlink scenario. We propose and model a NOMA slicing system where the medical data are categorized and assigned to two different slices based on 5G services. That is, 4K video from patients is assigned to an enhanced mobile broadband (eMBB) NOMA slice in both uplink and downlink, and all other medical data are assigned to an ultra-reliable and low latency communication (uRLLC) NOMA slice also in both uplink and downlink. Based on the system model and principles of NOMA, we formulate and use a joint power allocation optimization technique under users' minimum rate requirements and transmission power constraints, and successive interference cancellation (SIC) to maximize the medical data throughput as well as the system sum-throughput in each slice in both uplink and downlink. Our results show that, with the optimal power allocation technique, high throughput can be achieved for the 4K video and other medical data in the eMBB NOMA slice and uRLLC NOMA slice, respectively, but other users transmitting and receiving ordinary data in the slices will see their throughput decrease. Hence, in the interest of fairness for all users, we use truncated channel inversion power allocation in the downlink to prevent the decrease of the throughput of those users regardless of their channel conditions. INDEX TERMS 5G cellular network, network slicing, non-orthogonal multiple access (NOMA), power allocation, throughput maximization.