  Superconformal five dimensional theories have a rich structure of phases and
brane webs play a crucial role in studying their properties. This paper is
devoted to the study of a three parameter family of SQCD theories, given by the
number of colors $N_c$ for an $SU(N_c)$ gauge theory, number of fundamental
flavors $N_f$, and the Chern Simons level $k$. The study of their infinite
coupling Higgs branch is a long standing problem and reveals a rich pattern of
moduli spaces, depending on the 3 values in a critical way. For a generic
choice of the parameters we find a surprising number of 3 different components,
with intersections that are closures of height 2 nilpotent orbits of the flavor
symmetry. This is in contrast to previous studies where except for one case
($N_c=2, N_f=2$), the parameters were restricted to the cases of Higgs branches
that have only one component. The new feature is achieved thanks to a concept
in tropical geometry which is called stable intersection and allows for a
computation of the Higgs branch to almost all the cases which were previously
unknown for this three parameter family apart form certain small number of
exceptional theories with low rank gauge group. A crucial feature in the
construction of the Higgs branch is the notion of dressed monopole operators.
