"... I never heard "back in the day" in my life until five or ten years ago"

Same here.

I can't tell you who first said "back in the day" or why he or she said it.

But I believe that the "back in the day" saying came after "way back when" {or "way back then"}. And the equivalant phrase which preceded "way back when" was "the olden days".

So maybe someone took the "back" from "way back when" and the "day" from "the olden days" to coin the saying "back in the day".

Of course, there is also the saying "the good ole days".

Needless to say, the good ole days weren't always good.

But reminiscing makes them so.