I believe there were three emperors not mentioned here between Nero and Vespasian: Galba, Otho and Vitelius.
You’re right, but those guys only sat on the throne for a few months apiece, and it was a time of general upheaval and civil war. It wouldn’t have been surprising for a 1st century author to leave them out of a symbolic list like this.
well, they were there for a few months each in the time between AD 68 and 69 (the year of the 5 emperors)