The Orthodox are not Roman Catholic and the Dark Ages didn’t even happen to those areas of the world where the Orthodox church was predominant.
The Dark Ages specifically refers to the condition in Western Europe after the collapse of the Western Roman Empire in the fifth century, leading up to the collapse of the civil government of Rome in 600 AD, which left St. Gregory Diologos, who is a Roman Catholic who is venerated by the Eastern Orthodox, actually one of the last Roman Catholics to be venerated by the Eastern Orthodox before the schism, as the only high ranking public official left, and thus he was forced to negotiate with the Ostrogothic rulers who had conquered the city on behalf of the people of Rome to save as many lives as possible. Things were very grim. Then Charlemagne came along, and then the Medieval period and so on.
Meanwhile, the Eastern Roman Empire remained relatively stable, and a center of learning and cultural sophistication, and it continued to spread the Christian religion aggressively (and during this time the Western church did what it could as well, for example, converting the Angles, a tribe from an area which is now part of Denmark, who had conquered Britannia - indeed, all three Danish ethnic groups would wind up conquering England, along with the Saxons of Germany, in that the Angles were followed by the Jutes from Jutland, then the Saxons and then the Danish Vikings, who established the Danelaw ruled from Jarvik, which later became known as York, a beautiful town which I have visited, and home to the National Railway Museum in the UK as well as the splendid Yorkminster Cathedral (actually I visited York on one day in 2002, and the next day visited Brighton in the morning and Canterbury in the evening). But while that was going on in the West, the Eastern churches spread the faith throughout Eastern Europe, and to Eastern Scandinavia, and to the Southern Slavs and Bulgarians and finally the Northern Slavic people, the Kievan Rus, who are the ancestors of the Russians and Ukrainians (which is why i am so distressed by that war; its really more like the US Civil War than anything else).
The Byzantine civilization was glorious and impressive, and after losing some territories to the Ummayid Caliphate, managed to repel them using science, in the form of Greek Fire, a pyrophoric chemical weapon which could start fires on enemy ships which could not be extinguished, using flamethrowers, and which was also devastating against troops, and in this manner, and by forming alliances with the Kingdom of Armenia and the Armenian Kingdom of Cilicia, the Byzantine Empire was able to hold out until 1453, and a small part of it, Trebizond, on the Black Sea, was able to hold out even longer.
The Eastern Churches were never subordinate to the Pope of Rome, and indeed in many cases the reverse actually happened. For example, Pope Honorius I was censured post mortem by the Sixth Ecumenical Synod for supporting the heresy of Monothelitism. He is the only Bishop of Rome who was ever convicted of heresy by an ecumenical council.
Some Orthodox churches have been out of communion with Rome since the Council of Chalcedon in 451 (namely the Oriental Orthodox, that is to say, the Copts (Egyptians), Syriac Orthodox (Historically speakers of Aramaic dialects who live in Syria, Iraq, Turkey, the Holy Land and especially India, where they are known as St. Thomas Christians because the Gospel was first brought there by St .Thomas the Apostle, who was martyred by an enraged maharaja who threw a javelin at him). The rest broke off communion with Rome in the eleventh century.
Then when the Crusades happened, these had a devastating effect on the Orthodox Christians, indeed, in the First Crusade, the Crusaders even engaged in cannibalism of the local Christians when their supplies ran low.
So indeed, the Orthodox are not Roman Catholics, we disagree with them on many issues of theology, and it is very offensive to us to be grouped together with them.
Also, by the way, the period of time while Western Europe was in the so-called Dark Ages is still quite interesting, although not as interesting as what was going on in the Byzantine Empire at the same time, which was indeed very much in its prime, to the extent that during the Dark Ages, the Byzantine Empire actually occupied some portions of the former Western Roman Empire in order to reduce the suffering of the people, who were suffering the depradations of various Gothic tribes that had been converted to Arianism, which is the anti-Christian religion that originated with the heretic Arius in the early fourth century, and indeed, it was the cause for convening the Council of Nicaea, to ratify the decision of the Church of Alexandria to depose Arius.
However, Emperor Constantine’s son Constantius was converted to Arianism through the sinister machinations of Eusebius of Nicomedia, an Arian bishop who did not attend Nicaea but rather lurked in the shadows and climbed the power structures in Constantinople, and the result of this was an almost continual persecution of Christians by the Arian emperors from the death of St. Constantine until the death of Emperor Valens, who was the last of the Arian Emperors, at which time St. Theodosius became Emperor, around 379 AD, and the Second Ecumenical Synod was convened in Constantinople to address additional theological issues that had come up, such as Pneumaatomacchianism - denial of the deity and the distinct personhood of the Holy Spirit as a member of the Trinity.