In this talk, I will discuss the generalised and basic fuzzy 4-sphere in the context of the IKKT matrix model. These spaces arise as SO(5)-equivariant projections of quantised SO(6) coadjoint orbits and exhibit full SO(5) covariance. I will sketch how (basic and generalised) 4-sphere arise as solutions in a Yang-Mills matrix model, such that the fluctuations on the 4-sphere lead to a higher-spin gauge theory.