In this talk, we show some results on the existence and orbital stability of the peak-standing-wave solutions for the cubic-quintic nonlinear Schr\"odinger equation with a point interaction. Via a perturbation method and continuation argument, we obtain stability results in the case of attractive-attractive and attractive-repulsive nonlinearities. In the case of an attractive-attractive case and an focusing interaction we give an complete approach for stability based in the extension theory of symmetric operators.