We investigate the two-dimensional spatially inhomogeneous cubic-quintic nonlinear Schr(o)digner equation with different exteal potentials.In the absence of exteal potential or in the presence of harmonic potential,the number of localized nonlinear waves is associated not only with the boundary condition but also with the singularity of inhomogeneous cubic-quintic nonlinearities; while in the presence of periodic exteal potential,the periodic inhomogeneous cubic-quintic nonlinearities,together with the boundary condition,support the periodic solutions with an arbitrary number of circular rings in every unit.Our results may stimulate new matter waves in high-dimensional Schr(o)digner equations with spatially modulated nonlinearities.