Interacting unitary conformal fixed points in five dimensions are mysterious objects which often do not have weakly coupled UV descriptions. Their conformal data such as operator spectrum and correlation functions appear more elusive to conventional methods than in lower dimensions. In this talk, we make progress towards addressing this question using supersymmetry and a combination of techniques including localization, conformal bootstrap and holography.

We first discuss subtle properties of the sphere partition function of 5d N=1 superconformal field theories (SCFT) and derive formulae for conformal and flavor central charges from its deformations. Along the way, we discover a new superconformal anomaly in five dimensions. We then focus on the rank one Seiberg-Morrison E_n SCFTs, compute their central charges from IR gauge theory descriptions and clarify the notion of symmetry enhancement at the level of the sphere partition function. Finally we apply bootstrap methods to these theories and observe their saturation of the numerical bounds, which allows for solving the non-BPS spectrum. We also extend the analysis to the large (rank) N versions of these theories and compare with supergravity duals via AdS/CFT.