The purpose of this note is to introduce a new method for proving the existence of \Se metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new \Se metrics on $\scriptstyle{S^2\times S^3}$ and on $\scriptstyle{(S^2\times S^3)\# (S^2\times S^3).}$ These give the first known examples of nonregular \Se 5-manifolds. Our method involves describing the \Se structures as links of certain isolated hypersurface singularities, and makes use of the recent work of Demailly and Koll\'ar who obtained new examples of K\"ahler-Einstein del Pezzo surfaces with quotient singularities.