Does within 3 points of victory mean you have 5 points already?

Yes — being at 5 points or higher counts as "within 3 points of the Victory Score," since the Victory Score is 8 by default (8 − 3 = 5). So 5, 6, 7, and even 8+ all satisfy the condition; it's a threshold, not exactly 5.

Two things worth pinning down: the Victory Score is mode-dependent (11 in 2v2, so "within 3" there means 8+), and the check is a continuous state of the game rather than something measured only during a cleanup — so Find Your Center's discount and Leona, Zealot entering ready both turn on the moment the opponent's point total hits that threshold. Corrupted Dragon is the inverse: it enters ready only while your score is 4 or less.