What period did the first Cleopatra live in?

We don't know for certain because we don't know who the first Cleopatra was. Cleopatra was a very common Macedonian name. The first Cleopatra of Egypt, though, was the wife of Ptolemy V. However she was a Syrian princess, the daughter of Antiochus of Syria. We know that she had two sons and a daughter and died in 176 BC.