The chaos and adaptive synchronization for a fractionalorder GenesioTesi system with fifth order nonlinearity were investigated. The stability of equilibrium points was studied, and the necessary condition for doublescroll attractor existence in the system was satisfied. The bifurcation and an interior crisis from singlescroll to doublescroll attractors were also found with the variation of derivative order. The minimum effective dimension for the system to remain chaos is 2.784 in commensurateorder case and 2.793 in incommensurateorder case. Furthermore, the adaptive synchronization of the system with uncertain parameters via backstepping approach was realized by designing appropriated controllers. Numerical simulations were carried out to demonstrate the effectiveness and flexibility for the controllers.