Biometric authentication is currently used in almost all areas of digital media, such as mobile phones, laptops, attendance systems, and even in some restricted areas where access is granted based on biometric attributes such as fingerprints, iris patterns, etc. Therefore, the need to develop secure storage and transmission of biometric images across public networks is paramount in today’s world. This study presents a novel approach to biometric image encryption using a hyper chaotic map. A 5-D hyper chaotic system is proposed as a solution to the problems of diffusion and confusion, with the added advantage of providing a large key space. This method relies heavily on chaotic sequences generated by the 5-D chaos system. These sequences ensure a strong level of encryption by modifying and reorganizing pixel values throughout the image. Numerical simulations were conducted to demonstrate the validity and effectiveness of the proposed encryption scheme. The security analysis results confirm that the proposed encryption scheme is strong against brute force, differential, and statistical attacks.