I always thought that the historical chronology of Babylon 5 is rather inconsistent.
The universe is believed to be over 13,000,000,000 years old, and if I remember correctly that was also the scientific belief when MJS was creating the basic plot for Bablyon 5 sometime back in the 1980s.
Humans consider themselves and their immediate ancestors to be the first species of intelligent life to ever evolve on Earth. Earth was formed about 4,600,000,000 years ago, and developed an oxygen rich atmosphere suitable for large, multi celled land animals to breath when it was about 4,000,000,000 years old.
And it seems perfectly possible that a star system with planets could have formed 8,600,000,000 to 9,200,000,000 years ago with just as much heavy elements as our solar system and planets have,and intelligent life could have evolved on one of the planets 4,600,000,000 years ago.
And it is possible that the first intelligent beings might have evolved on various planets in the universe 5,000,000,000, or 6,000,000,000, or 7,000,000,000, years ago.
The Vorlons and the Shadows are two species of the First Ones, the earliest intelligent beings in the universe. The first First One was allegedly the immortal Lorien, the first of his species.
Lorien makes the statement that he is not a First One but rather the First One, belonging to a nearly immortal race of great wisdom and power, and, according to himself, the first being to achieve sentience in the universe. It was his race that discovered and nurtured many of what the Humans and Minbari refer to as the First Ones, including the Vorlons and the Shadows.
Lorien claims that "the universe" created him as an immortal intelligent being, but later switched to creating mortal intelligent beings.
Since intelligent being could have evolved in other star systems billions of years ago, and since Lorien claims that "the Universe" created him and some of the other intelligent lifeforms deliberately, and thus possibly long before it was possible for intelligent beings to evolve naturally, it is possible that the First Ones, including the Shadows and the Vorlons, have existed for five or ten billion years, for example.
Suppose that the Shadows and the Vorlons began fighting their proxy wars "only" one billion, or 1,000,000,000, years ago.
If the average interval between those wars was one million years, they would have fought one thousand such wars, with only the latest three known to characters in Babylon 5.
If the average interval between those wars was one hundred thousand years, they would have fought ten thousand such wars, with only the latest three known to characters in Babylon 5.
If the average interval between those wars was ten thousand years, they would have fought one hundred thousand such wars, with only the latest three known to characters in Babylon 5.
If the average interval between those wars was one thousand years, they would have fought one million such wars, with only the latest three known to characters in Babylon 5.
And I can't help thinking that the more such proxy wars that were fought, the greater the probability would be that the younger races would have thought of telling the Shadows and Vorlons to go away and leave them alone. It seems to me highly improbable that the Shadows and the Vorlons would still be at it after hundreds or thousands of such proxy wars.
The fact the Shadows and the Vorlons are still fighting proxy wars in the era of Babylon 5 makes me suspect that the war about 10,000 earlier might have been the first war, or second war, or third war, or something. I find it hard to believe that the Shadows and Vorlons have been fighting proxy wars via the younger species for hundreds of millions, or billions, of years.
Anyway, I find the historical chronology of babylon 5 to be rather vague and insistent, and so I doubt that anyone, not even MJS himself, can give a good answer to the question of how long the Shadows and Vorlons were at war.