  We study the dynamics of M-theory on isolated non-toric Calabi-Yau threefold
singularities of type $(A_j,A_l)$ and $(A_k,D_n)$, engineering five-dimensional
rank-zero SCFTs. Our approach consists in mapping these backgrounds to type IIA
string theory with D6 branes at angles and O6$^{-}$ planes, computing the
five-dimensional open string modes located at the brane intersections. This
permits us to characterize the Higgs Branches of these theories as algebraic
varieties, determine the flavour and gauge group and inspect subtleties related
to T-branes. Our methods apply for all the considered singularities: we give a
closed formula for the $(A_j,A_l)$ Higgs Branches, and tables for the Higgs
Branches of the $(A_k,D_n)$ series.
