This paper presents the construction of a 5D Euler equation using four sub-Euler equations with the coupling parameters and analyzes the conservation of Hamiltonian and Casimir energy. By breaking the conservation of Casimir energy, a 5D Hamiltonian conservative hyperchaotic system is developed. Phase diagrams, Lyapunov exponent spectra, and bifurcation diagrams are employed to investigate the nonlinear properties of the system. It is discovered that the system possesses dynamic characteristics such as amplitude control, multistability, transient quasi-period, and a wide constant range. The statistical properties of the pseudo-random sequences produced by the system are assessed via the National Institute of Standards and Technology (NIST). Lastly, the circuit simulation and STM32 platform are used to confirm the viability of the system.