Projective group properties of $h$-spaces of type $\{221\}$

We investigate the curvature of a 5-dimensional $h$-space $H_{221} $ of the type $\{221\}$ [3], necessary and sufficient conditions are obtained in order that $ H_ {221} $ be a space of constant curvature $K$ (theorem 1). A general solution of the Eisenhart equation is found in the $h$-space $H_ {221}$ of non-constant curvature. The necessary and sufficient conditions for the existence of non-homothetical projective motion in the $h$-space $ H_{221} $ of non-constant curvature are established (theorem 5) and, as a consequence, the structure of the non-homothetical projective Lie algebra in such a space is determined (theorem 6).