Why did Peter and John go up to the temple at the hour of prayer in Acts?
They went because they were still observing Judaism under the Law, not because Christianity required temple prayer. Even as believers in Christ as Messiah, they had not been released from the Law's demands. The early chapters of Acts depict Israel still under legal temple worship and prayer practices.
Les explains that Jesus' entire three-year earthly ministry was to the Jew and under the Law. He never told anybody to stop temple worship, and He never told a Jew they no longer had to give sacrifices. Even after Christ's death, burial, and resurrection, the early chapters of Acts still show Jews under the Law; no one had told them they were not under the Law, and everything was still legal. So when Peter and John go up to the temple at the hour of prayer in chapter 5, it implies they were practicing Judaism, not a Christian requirement, since nothing in Christianity demanded going to the temple three or four times a day to pray. They were still under the demands of the Law even though they had recognized Christ as their Messiah and believed, and were not released from the Law. Les points out that those early chapters of Acts are still God dealing with the nation of Israel, and the language is plain.
Now Peter and John went up together into the temple at the hour of prayer, being the ninth hour.