  We study the Swampland Distance Conjecture for supersymmetric theories with
AdS${}_5$ backgrounds and fixed radius through their $\mathcal{N}=2$ SCFT
holographic duals. By the Maldacena-Zhiboedov theorem, around a large class of
infinite-distance points there must exist a tower of exponentially massless
higher-spin fields in the bulk, for which we find bounds on the decay rate in
terms of the conformal data. We discuss the origin of this tower in the gravity
side for type IIB compactification on $S^5$ and its orbifolds, and comment
about more general cases.
