He had a very long stable reign, expanded the empire, "found Rome in brick and left it in marble" etc. And I know that he was a master propagandist and he killed off most of the people that opposed him(but this one was before he became emperor), but he still deserves a spot here in my opinion.
I think the best explanation in this case is the simplest one: the term “5 Good Emperors” refers specifically to the chronological succession of five emperors (Nerva, Trajan, Hadrian, Antonius Pius, and Marcus Aurelius) who were lauded for their expansion of the empire and the relative stability of their reigns. It’s not simply a list of “the five best Emperors of Rome — number 4 will shock you!” it’s a non-dynastic succession of notable emperors. Augustus is widely regarded as a successful and comparable emperor, but he wasn’t part of the succession that involved the aforementioned 5, he reigned much earlier and as part of the Julio-Claudian dynasty.