By performing the femtosecond-pulsed [Formula: see text]-scan experiments at a wavelength of 780[Formula: see text]nm, we report the observation of simultaneous third- and fifth-order refractive nonlinearities in the film of a side-chain azobenzene copolymer synthesized by free-radical polymerization method. Theoretically, we extend two continuous wave [Formula: see text]-scan theories suitable for the excitation of ultrafast laser pulses. First one is valid only for the situation of the sample with the pure third-order refractive nonlinearity. Second one is applicable when the sample exhibits the simultaneous third- and fifth-order refractive nonlinearities. Both [Formula: see text]-scan theories allow the precise analysis of femtosecond-pulsed [Formula: see text]-scan experimental data. Using the femtosecond time-resolved optical Kerr effect measurements, we estimate the nonlinear response time of the sample to be in the sub-picosecond regime. The physical mechanisms of the observed nonlinearity are also discussed. The high nonlinear figure of merit with ultrafast response in this polymer is desirable in nonlinear photonic devices.