(Joint work with Yiqi Huang). We refine the regularity of non-collapsed limits of Einstein 5-manifolds. In particular, we show uniqueness of tangent cones on the full top stratum, show that the structure of the singular set lies in countable unions of Lipschitz curves and points. We finally prove real-analytic orbifold regularity along curves of singularities, which are also proven to be geodesics, and establish uniqueness of tangent cone at infinity under Euclidean volume growth with a line split. The proofs rely on new 4- dimensional gap/isolation theorems for spherical and hyperbolic Einstein orbifolds.