  We propose two novel methods for computing the superconformal index of 5d
superconformal field theories that cannot be described by conventional
Lagrangian descriptions under mass deformations. The first approach involves
the use of Higgs branch flows from UV Lagrangian theories, guided by
transitions in 5-brane webs in Type IIB string theory. The second method
employs the relationship between O$7^+$-plane and O$7^-$-plane with eight
D7-branes, which applies to particular non-Lagrangian theories realized by
brane configurations involving an O$7^+$-plane. As a concrete application of
our method, we compute the superconformal indices for all known rank-1
non-Lagrangian theories, which we also use to identify flavor symmetries and
their global forms at the conformal field theory (CFT) fixed points.
