A novel fifth-order hyperchaotic circuit is proposed. This circuit is composed by three linear inductors, two linear capacitors, one negative resistor, and two nonlinear elements, and has the π type circuit configuration. By switching the time constant of the circuit by the action of nonlinear element, the voltage and current is rapidly changed, and by using negative resistors, the condition for local divergence in the circuit is satisfied. The rapid change of voltage and current and local divergence are two primary conditions for generating chaos and hyperchaos in the circuit. Bifurcation and Lyapnuov exponent calculations demonstrate that the oscillation mechanism of the circuit evolves into chaos and hyperchaos from periodic with the change of bifurcation parameters. Furthermore, the fifth-order hyperchaotic circuit has been designed and the result of hardware experiment is reported.