$N^3$-behavior from 5D Yang-Mills theory

In this note we derive $N^3$-behavior at large t’ Hooft coupling for the free energy of 5D maximally supersymmetric Yang-Mills theory on $S^5$. We also consider a $Z_k$ quiver of this model, as well as a model with $M$ hypermultiplets in the fundamental representation. We compare the results to the supergravity description and comment on their relation.