  The five-dimensional $\mathcal{N}=1$ supersymmetric gauge theory with Sp(N)
gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes
with $N_f$ D8-branes on top of a single O8 orientifold plane in Type I' theory.
This theory is known to be superconformal at the strong coupling limit with the
enhanced global symmetry $E_{N_f+1}$ for $N_f\le 7$. In this work we calculate
the superconformal index on $S^1\times S^4$ for the Sp(1) gauge theory by the
localization method and confirm such enhancement of the global symmetry at the
superconformal limit for $N_f\le 5$ to a few leading orders in the chemical
potential. Both perturbative and (anti)instanton contributions are present in
this calculation. For $N_f=6,7$ cases some issues related the pole structure of
the instanton calculation could not be resolved and here we could provide only
some suggestive answer for the leading contributions to the index. For the
Sp(N) case, similar issues related to the pole structure appear.
