  We propose a number of apparently equivalent criteria necessary for the
consistency of a 5d SCFT in its Coulomb phase and use these criteria to
classify 5d SCFTs arising from a gauge theory with simple gauge group. These
criteria include the convergence of the 5-sphere partition function; the
positivity of particle masses and monopole string tensions; and the positive
definiteness of the metric in some region in the Coulomb branch. We find that
for large rank classical groups simple classes of SCFTs emerge where the bounds
on the matter content and the Chern-Simons level grow linearly with rank. For
classical groups of rank less than or equal to 8, our classification leads to
additional cases which do not fit in the large rank analysis. We also classify
the allowed matter content for all exceptional groups.
