  We formulate geometric conditions necessary for engineering 5d superconformal
field theories (SCFTs) via M-theory compactification on a local Calabi-Yau
3-fold. Extending the classification of the rank 1 cases, which are realized
geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose
an exhaustive classification of local 3-folds engineering rank 2 SCFTs in 5d.
This systematic classification confirms that all rank 2 SCFTs predicted using
gauge theoretic arguments can be realized as consistent theories, with the
exception of one family which is shown to be non-perturbatively inconsistent
and thereby ruled out by geometric considerations. We find that all rank 2
SCFTs descend from 6d (1,0) SCFTs compactified on a circle possibly twisted
with an automorphism together with holonomies for global symmetries around the
Kaluza-Klein circle. These results support our conjecture that every 5d SCFT
can be obtained from the circle compactification of some parent 6d (1,0) SCFT.
