In this dissertation, we discuss two results relevant to the study of five-dimensional super- conformal field theories. In the first half of this work, we use six-dimensional Euclidean F(4) gauged supergravity to construct a holographic renormalization group flow for a supercon- formal field theory on S5. Numerical solutions to the BPS equations are obtained and the free energy of the theory is determined holographically by calculation of the renormalized on- shell supergravity action. A candidate field theory dual to these solutions is then proposed. This tentative dual is a supersymmetry-preserving deformation of the theory engineered via the D4-D8 system in string theory. In the infrared, this theory is a mass deformation of a USp(2N) gauge theory. A localization calculation of the free energy is performed for this infrared theory, and is found to match the holographic free energy.

In the second half of this work, we establish a close relation between recently constructed AdS6 solutions in Type IIB supergravity, which describe the near-horizon limit of (p,q) 5-brane junctions, and the curves wrapped by M5-branes in the M-theory realization of the 5-brane junctions. This provides a geometric interpretation of various objects appearing in the construction of the Type IIB solutions and a physical interpretation of the regularity conditions. Conversely, the Type IIB solutions can be used to obtain explicit solutions to the equations defining the M-theory curves associated with (p,q) 5-brane junctions.