To further study memristors and their applications, a smooth five-dimensional memristive hyperchaotic system with hidden attractors is proposed. Chaotic characteristics of the system are verified by depicting phase diagrams and the Lyapunov exponent spectrum. The bifurcation parameter of the system is analyzed, and the offset boosting of two state variables is realized. The amplitude control of the attractor is analyzed. The extreme multistability phenomenon in the system is also found based on initial values. When initial values move along the x
-axis, and different straight lines in the x-u
plane, new phenomena on the offset boosting of the attractors are revealed. Finally, a nonlinear circuit simulation equation of the system is established, verifying the feasibility of physical realization using the derived flux-controlled memristor system.