Discrete θ and the 5d superconformal index

5d Yang-Mills theory with an Sp(N) gauge group admits a discrete analog of the θ 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 E₁ theory.