The exponential advancement witnessed in 5G communication and quantum computing has presented unparalleled prospects for safeguarding sensitive data within healthcare infrastructures. This study proposes a novel framework for healthcare applications that integrates 5G communication, quantum computing, and sensitive data measurement to address the challenges of measuring and securely transmitting sensitive medical data. The framework includes a quantum-inspired method for quantifying data sensitivity based on quantum superposition and entanglement principles and a delegated quantum computing protocol for secure data transmission in 5G-enabled healthcare systems, ensuring user anonymity and data confidentiality. The framework is applied to innovative healthcare scenarios, such as secure 5G voice communication, data transmission, and short message services. Experimental results demonstrate the framework’s high accuracy in sensitive data measurement and enhanced security for data transmission in 5G healthcare systems, surpassing existing approaches.