I don't have enough background to give an educated and justified person for every century from the 5th century BC to the 19th century (I'm assuming A.D.?), however using my current knowledge I'll give my opinion and justification for a few of the requested centuries:

3rd Century A.D.: Emperor Diocletian of Rome. After years and years of civil war during the 3rd century where any military general with a substantial army under his command could march to Rome and be declared emperor by the senate. If my memory serves me right, there were about 27 emperors in a period of about 47 years. Of these 27 emperors, only one died in his bed. The rest either died in battle or were assassinated. Diocletian, when he came to power in 284 A.D, was the first emperor to be able to hold power for more than a few years in a long time. He realized that in order to return Rome to stability and it's previous glory, power would need to be split up because one man is not enough to control the entire Empire. He split the power of the emperor into 4 different people, consisting of two Augustuses (emperors) and two Caesars (co-emperors), one Augustus and one Caesar for each half of the empire. Along with this, he also split the power of the provinces of Rome in half, with there now being two Governors per province. He also reformed the military and how Rome's borders were defended.

4th Century A.D.: Emperor Constantine of Rome. Following suit with Diocletian, Constantine officially split the empire into two different Empires. The Roman Empire of the west and the east. He moved the capital city of the empire to a brand new city named after himself: Constantinople. He changed the religion of the empire to Christianity. His new empire and it's capital continued to live on for another ~1000 years while the western empire struggled and eventually fell victim to the invasion of the Germanic tribes and the pressures of Islam.

8th Century A.D.: Easily emperor Charlemagne of the Carolingian Empire. Charlemagne was a great military commander that conquered new territory including the Saxons, the Lombard Kingdom, and others. He established a, though short living, powerful empire by means of his military power and a system of being able to rule territories remotely. He was the people's hope to return the world to a single, unified, peaceful empire. Even though his heirs would be unable to continue his legacy, he assisted in what will eventually become modern Europe.

9th Century A.D.: Sorry, I have to pick two people for this one. King Louis the German, and King Charles the Bald. I was debating picking Alfred the Great of the Anglo-Saxon empire, however I think these two have had a larger impact on modern Europe. Anyways, these two of Louis the Pious' sons fought a civil war among each other for power of the Carolingian Empire during and after their father's death. They came upon agreement that Charles the Bald would control the western third of the empire, and Louis the German would get the eastern third of the empire. Even though they didn't do a very good job at protecting and controlling their empires, these territories they formed went on to become modern Germany and France.

As for the 2nd and 3rd categories, I think it's a bit too bold to declare a singular person for an entire millennium of history.

That's all I really have time for at the moment, I could probably have come up with a few more if I had more time.