The whispering gallery mode （WGM） micro-resonator is an ideal platform for investigating the nonlinear light phenomenon. In this article， we achieved up to the fifth-order cascaded stimulated Brillouin scattering （SBS） light in a CaF₂ micro-disk resonator with an mm-sized 12.6 mm diameter and an ultra-high quality factor （ factor） at 1 550 nm wavelength. We found that there are multi modes of families in our large-scale micro-disk resonator when coupled to an adiabatic tapered fiber， which can easily select resonances matching the SBS frequency shift. This can eliminate the requirement that precisely controlls the scale of the resonator to match the free spectral range （FSR） with the Brillouin frequency shift. During our experiment， to solve the environmental fluctuation problem between the micro-disk resonator and tapered fiber， we designed a packaged platform that can steadily seal the resonator and tapered fiber in an N₂ atmosphere. The generated cascaded Brillouin light and the stable packaged platform can further be used to investigate the multi-wavelength Brillouin laser and Brillouin light-based gyroscope.