AT&T released UNIX Version 7 (seven) in 1979.
The same company released UNIX System V (five) in 1983.
Why did the later release have a lower number?
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There is not a single Unix line ('Unix' is not unique). The numbers measure different things. Anyone who forked a variant of Unix was free to start a whole new sequence of numbering.
Seventh edition Unix came from the 'classic' Unix lineage out of Bell Labs, latterly known as 'Research Unix'.
Meanwhile, presumably because of its flexibility, there were many offshoots from the original, under various divisions or departments. In particular for this answer, the Unix Support Group (USG) developed a commercialized Unix system. System III contained features from several different Unixes: 7th ed. Unix, PWB/UNIX 2.0, CB UNIX 3.0, UNIX/RT and UNIX/32V.
Per Wikipedia, the system was apparently called System III because it was considered the outside release of UNIX/TS 3.0.1 and CB UNIX 3.
System V followed on from System III (System IV never seems to have emerged in public).
But to state my answer differently, there's no reason why the number sequence of the commercial "System N" variants should follow on from the numbers used by Bell Lab's "N'th edition" Unix.