We discuss the large N factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form M = M 3 × S 2 , where is an equivariant parameter for rotation. We show that, when M 3 is a squashed three-sphere, the large N partition functions can be obtained by gluing elementary blocks associated with simple physical quantities. The same is true for various observables of the theories on M 3 = Σ g × S 1 , where Σ g is a Riemann surface of genus g, and, with a natural assumption on the form of the saddle point, also for the partition function, corresponding to either the topologically twisted index or a mixed one. This generalizes results in three and four dimensions and correctly reproduces the entropy of known black objects in AdS 6 × w S 4 and AdS 7 × S 4 . We also provide the supersymmetric background and explicitly perform localization for the mixed index on Σ g × S 1 × S 2 , filling a gap in the literature.