According to this discussion on the Stack Exchange site, the five-fold repetition automatically ends the game, regardless of subsequent play. Apparently this is because of Rule 6.2a.
https://chess.stackexchange.com/questions/6194/quintuple-repetition-and-the-fides-2014-rulebook-revision
Is mate after fivefold repetition still valid?
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Jul 30, 2018
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#2
The laws since this year:
9.6
If one or both of the following occur(s) then the game is drawn:
9.6.1
the same position has appeared, as in 9.2.2 at least five times.
9.6.2
any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence.
Checkmate is expressly mentioned as taking precedence in 9.6.2, over 75 moves - but is NOT mentioned in point 9.6.1 as taking precedence over fivefold repetition!
Does it mean that if a game is eventually interrupted by checkmate, resignation or flag fall, but on rereading the scoresheet it appears that any position/s have appeared 5 or more times, the game having been automatically drawn on the first occasion a position appeared 5th time takes precedence over any subsequent checkmate, resignation or flag fall?
9.6.2 expressly confers precedence on checkmate over 75 moves. Do resignation and flag fall take precedence over 75 moves, or do they by omission not have such precedence?