||In this paper, chaos and adaptive synchronization for a fractional-order Genesio-Tesi system with fifth order nonlinearity are investigated. The minimum effective dimension for the system to remain chaotic is 2.784 in the commensurate-order case and 2.793 in the incommensurate-order case. A period-doubling bifurcation and an interior crisis from single-scroll to double-scroll attractors are also found with the variation of derivative order. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization of the system with unknown parameters is realized by designing appropriated controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.