PS: I thought that according to this, questions in Chinese were allowed, but I can't publish it without English...
I think “一” might originally mean “slight(ly)”, “mere(ly)” or “just”, but it's commonly used in various constructions where its original meaning is not preserved.
After thinking for a day, I feel that this “一” might have been derived from “the first” or “the beginning”.
I feel “一” often signals the beginning of a significant change, or some special event. It's also used to form nominal phrases. e.g. “一别” can function like a noun.
Nevertheless, “一” is mainly used in classic Chinese and retained in fixed expressions, e.g. 一…就…, 一…,…了. When we use it, we tend to understand the structure as a whole, without thinking the meaning of any individual word.
In general its meaning is same as "分别", usually used to emphasize the time was so long.
this separation being 5 to 6 years
一should be understood as 一旦(as long as, since).
“一别” means the time since we left from each other.
“一别五六年”：“五六”——we cannot translate it as the chinese characters as "five" or "six", this just meeans for ages or long time. So the correct translation of “一别五六年” should be:
It's been for ages since we left from each other.
PS：We Chinese usually use some numbers to describe something special, here the "numbers" aren't used for count. Let's take some samples:
1)七上八下：(Pretty unsure because of being worried, meaning “六神无主”、“忐忑不安”)