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While other lines have their names, such as the line of influence for the 4th line, I haven't heard of one for the 5th line up until tonight, where I heard an expert call it the line of vagueness.
It may have been said partly in jest, but I think that vagueness isa suitable name for the 5th line.
From first to fifth then that would make them, Death, Defeat, Territory, Influence, and Vagueness.
Maybe the Line of Emptiness is a bit snappier?
Though really, the 5th line is much like the 6th is much like the 7th, so it seems awkward to give the 5th line a special name. With the exception of an occasional corner move, we don't usually try to play 5th line moves as fuseki.