  We systematically analyse 5d superconformal field theories (SCFTs) obtained
by dimensional reduction from 6d $\mathcal{N}=(1,0)$ SCFTs. Such theories have
a realization as M-theory on a singular Calabi-Yau threefold, from which we
determine the so-called combined fiber diagrams (CFD) introduced in
arXiv:1906.11820, arXiv:1907.05404, arXiv:1909.09128. The CFDs are graphs that
encode the superconformal flavor symmetry, BPS states, low energy descriptions,
as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from
6d, there are two approaches: the first is to consider a circle-reduction
combined with mass deformations. The second is to circle-reduce and decouple an
entire gauge sector from the theory. The former is applicable e.g. for very
Higgsable theories, whereas the latter is required to obtain a 5d SCFT from a
non-very Higgsable 6d theory. In the M-theory realization the latter case
corresponds to decompactification of a set of compact surfaces in the
Calabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descend
from non-Higgsable clusters and non-minimal conformal matter theories. Finally,
inspired by the quiver structure of 6d theories, we propose a gluing
construction for 5d SCFTs from building blocks and their CFDs.
