If I'm in control of both battlefields with Ahri Alluring at 5 points, during my beginning phase when I score for holding, does the extra point from Ahri allow me to win the game?

Yes, you win the game.

You start at 5 points and control both battlefields. During your Beginning Phase, holding the first battlefield scores 1 point (→6), then holding the second scores 1 point (→7). Ahri, Alluring's triggered ability — "When I hold, you score 1 point" — fires from whichever battlefield she's at and scores a 3rd point (→8), immediately winning you the game.

The final-point restriction only applies to conquering (Rule 466.1.a.1). Points from other sources like Ahri's triggered ability are not beholden to that restriction and can win the game directly (FAQ #10243, #2646, #1936).