We study the new spatial optical solitons and their propagating properties in the one-dimensional nonlocal cubic-quintic (C-Q) nonlinear model by the numerical method. We obtain multi-bright solitons and multipole soliton solutions in the one-dimensional nonlocal C-Q nonlinear model. The propagation of bright solitons is stable in the competing nonlocal cubic self-defocusing and quintic self-focusing nonlinear media when these nonlocal and nonlinear parameters are in the appropriate value domain. Considering the different nonlinear cubic effects, the interaction between two optical solitons with the same phase in the general nonlocal media displays the attraction or the repulsion for different nonlocal and nonlinear parameters. We find that the interval of two solitons affects the interaction between them. The refractive index is changed with the propagating constant when the nonlocal constant d3 is 10. Moreover, the triplepole, quadrupole and pentapole solitons can propagate steadily when the nonlocal parameters are appropriate, but hexa-pole (or above) solitons propagate unsteadily for any nonlocal parameter. Furthermore, we investigate the multi-pole solitons and their propagation stabilities by the Newton difference method and the Fourier split step method, obtain the stable propagation conditions for dipole, triplepole and quadrupole solitons, and find that the propagation of the pentapole and higher-order pole solitons is unstable. We also discuss the interactions of multi-pole solitons when they propagate along the axis z. The interactions are attraction or repulsion when the nonlocal and the nonlinear parameters are different. Meanwhile, we simulate the evolution of the refractive index along the axis z when the spatial optical solitons are multi-pole solitons. Finally, we study the relation between the power of soliton and the propagation constant under different degree of nonlocality. The power of the single bright soliton does not monotonically increase with the increasing propagation constant when the degree of nonlocality d3 is 10. We also derive the relation between the power of dipole bright solitons with the cubic nonlinearity parameter and the propagation constant under different degree of nonlocality. The power decreases monotonically with the increasing propagation constant when the cubic nonlinearity is a certain value or with the increasing cubic nonlinearity when the propagation constant is a certain value.