5 Rings of Moscow is a relatively recent race. The Tour of the USSR was a much earlier event that tended to run over two weeks.
The most important race over that side of Europe was the Friedensfahrt, though the DDR-Rundfahrt and Tour de Pologne were both prestigious as well. There were some key one-day races as well (Berlin-Cottbus-Berlin and the Rund um Berlin are particularly notable). The Soviets had two eras of domination, one in the mid-60s with names like Gennady Lebedev, Alexey Petrov and Gainan Saydkhuzhin, and one from the mid 70s to the early 80s with Aavo Pikkuus (an Estonian all-rounder with a killer ITT and who wore the leader's jersey start to finish in the 1977 race before retiring a few years later to take up rally driving aged 27), Yuri Barinov, Shakhid Zagretdinov, Aleksandr Averin and the aforementioned Sergey Sukhoruchenkov (who was the greatest climber the Eastern Bloc ever produced, by some distance, winning the Olympics in 1980 with a stupendously long range attack (he in fact attacked at km 0 to stay with a select group for a while before soloing in from miles out), Avenir twice, Regioni, and nearly anything mountainous that he entered - unfortunately there just weren't enough hilly races in the Ostbloc back then and the number of strong Soviet riders meant he didn't always get selections if courses didn't suit him) all winning the Friedensfahrt in a period from 1977 to 1981, with Soukho winning again in 1984; at the same time you had monster Estonian sprinter/cobbled hardman Riho Suun, and break specialist Oleg Chuzhda (father of the current Oleg Chuzhda) who podiumed the race in a surprise result in 1983. Ivan Mishchenko was also a very strong Soviet rider at the time, however the mid-80s saw a revamped DDR team take over as the foremost Ostbloc team, what with Olaf Ludwig winning a sprint at the end of every brutal flat stage (at least until Abdoujaparov showed up in the late 80s), Uwe Ampler (son of former Peace Race winner Klaus) killing everybody in the chrono, and Uwe Raab, Falk Boden, Jan Schur (son of East Germany's favourite sportsman and one of the Ostbloc's greatest ever riders, Täve Schur) and Olaf Jentzsch the rest of the time (not to mention that arguably their best rider, Wolfgang Lötzsch, was kept out of teams much of the time owing to his perceived unreliability due to political beliefs). The Soviets still had enough strong riders to make an impact with the likes of Ugrumov and Abdou though.
The Friedensfahrt did head to the Soviet Union twice though, first in 1985 (it had a Prologue in Prague, then travelled to Moscow for three stages before returning to Prague for its usual three capitals), then in 1986 (perhaps the most notorious Friedensfahrt craziness - the politics that fuelled the event would make an interesting subject all of their own, and this was the zenith - the opening four days being spent in Kiev, just after the Chernobyl disaster. All Western teams bar the French and the extremely loyal Finns (they entered the Friedensfahrt on 39 separate occasions without a single stage win to their name) withdrew before the race leaving its smallest péloton in years; major riders from the bigger nations were given no illusions that choosing not to take part would not adversely affect their careers.
The Ostbloc riders mostly showed up in major amateur events and the open races of the mid-70s onwards. After the first "glory days" of the event in the 50s, the standards in the East slipped a bit, and western amateurs won a fair few events in the late 60s (Marcel Maes, Bernard Guyot and Jean-Pierre Danguillaume winning the Peace Race outright between 66 and 69), however from the advent of the great Polish team of the early 70s, led by Ryszard Szurkowski, thought by many to be the greatest of all Iron Curtain cyclists, saw a real transformation in their fortunes. Being able to enter Paris-Nice one year was fascinating, when Szurkowski managed to finish 2nd only to Merckx in one stage, although he fell away on Mont Faron (28th overall in the end). However, that an amateur would come 2nd only to the great Cannibal was seen as a potential propaganda tool in the East and soon DDR, Czechoslovak and of course Soviet squads were entering amateur events in the West and acquitting themselves well; several other races in the West were also seeing the potential of being "open" events, allowing both the limited number of pro teams of the time to be padded out with amateurs (in practice meaning very strong cyclists from Eastern Europe showing up). As a result, you'll see major Ostbloc names all over results lists of races like Sarthe and Luxembourg in the late 70s and early 80s.
The history of cycling in the Eastern bloc is fascinating and it's really sad that a lot of it has been forgotten; because of its amateur nature, the race was naturally going to crumble in stature as soon as the biggest Ostbloc riders were allowed to turn pro, because many of the names that made it what it was couldn't ride anymore. And because of the politics, the race is rather looked back on through the eyes of the propaganda machines that fuelled it (most of which lost most of their funding and circulation post-Wende). And due to the limitation on being professional and the lower number and level of events riders would enter over there, it really would be interesting to see how the best riders of the era would have coped against the Westerners. We only occasionally got to see it.
Tour de l'Avenir 1982 - there's Sergey Sukhoruchenkov on the left, who won the race overall in 1978 and 1979 and is the only two-time winner of the race, and Greg Lemond in the middle.
We saw from the early 90s what a lot of the riders of the time of the
Wende could do when given a professional's time, effort and race calendar: the likes of Olaf Ludwig, Djamolidine Abdoujaparov, Piotr Ugrumov, Uwe Ampler and Dmitry Konyshev showed it. I just wish we could have seen what Jan Veselý, Täve Schur, Ryszard Szurkowski, Aavo Pikkuus or Sergey Sukhoruchenkov could have done with those same opportunities.