  5d Yang-Mills theory with an Sp(N) gauge group admits a discrete analog of
the theta parameter. We describe the origin of this parameter in N=1 theories
from Type I' string theory, and study its effect on the 5d superconformal fixed
point theories with an Sp(1)=SU(2) gauge group by computing the superconformal
index. Our result confirms the lack of global symmetry enhancement in the
so-called \tilde{E}_1 theory.
