We consider five dimensional N=1 Sp(1) gauge theory with no matter field based on a brane configuration with an O5-plane. It is known that two different theories exist depending on the discrete theta angle. We investigate how to realize the discrete theta angles by using (p,q) 5-brane and an O5-plane. We first devise a technique for computing Seiberg-Witten curves of the two theories based on the brane web with an O5-plane. Their Seiberg-Witten curves show that their corresponding M5-brane configurations under the presence of OM5-planes are different. The decompactification limit of each Seiberg-Witten curve also shows distinct phase structures in their Coulomb branch leading to significantly different (p,q) 5-brane configurations with an O5-plane in the ``past infinite coupling region''.