Final answer:
The "Five Good Emperors" innovated by establishing a system where heirs were adopted based on merit, which contributed to the Roman Empire's period of stability and prosperity.
Step-by-step explanation:
The great political innovation of the "Five Good Emperors" was C) the establishment of adoption of heirs, based on merit and not family. This meritocratic system ensured that each emperor would adopt a younger man of proven abilities as his son, securing a competent succession. This system of choosing successors for their abilities rather than their bloodline helped maintain the stability and prosperity of the Roman Empire during its height.
In contrast to practicing nepotism, they built upon the foundational bureaucracy established by former emperors such as Augustus and continued to govern the empire efficiently. Emperors like Trajan expanded and strengthened the empire; with provincial elites sending their sons to Constantinople for education and positions, creating a blend of merit-based and sometimes nepotistic governance. However, this blend of bureaucratic competence and systematic adoption remained distinct during this period, promoting the empire's longevity and stability.