  We consider the nonlinear Schr\"odinger equation with a focusing cubic term
and a defocusing quintic nonlinearity in dimensions two and three. The core of
this article is the notion of stability of solitary waves. We recall the two
standard notions of orbital stability in the context of nonlinear Schr\"odinger
equations, and show that they must be considered as independent from each
other. We investigate numerically the notion of orbital stability of ground
states in the radially symmetric case, confirming existing conjectures or
leading to new ones.
