Based on Gaussian decomposition method, we present a theoretical investigation on the astigmatic Gaussian beam Z-scan when materials possess the simultaneous third- and fifth-order nonlinear refraction effects, and obtain an analytic expression of normalized transmittance of the Z-scan trace for the case of pinhole. The influences of ellipticity and waist separation on the Z-scan curves are analyzed. We find that normalized transmittance difference between the peak and the valley in Z-scan curves decreases gradually with the increment of the waist separation or with the decrement of the ellipt...
