A nonlinear controller is proposed to acquire generalised projective synchronization and arbitrary trajectories of full states of a fifth-order hyperchaotic circuit system. By adjusting the scaling factor and the accelerated factor, generalized projective synchronization between the fifth-order hyperchaotic circuit system and the hyperchaotic systems,chaotic systems and periodic signal can be rapidly realised, and the fifth-order circuit's hyperchaotic circuit system can also be driven to arbitrary periodic orbits or fixed point rapidly. Simulation results are presented to demonstrate the effectiveness of the proposed method.