[5nl FR] QK on QQ5 flop

Villain is 26/7/1 (147 hands) and usually doesn't bet without having it.
This is 5nl with possibility to buy in for $10.

BTN: $9.04 (180.8 bb)
SB: $5.80 (116 bb)
Hero (BB): $23.20 (464 bb)
UTG+1: $5 (100 bb)
MP1: $16.60 (332 bb)
MP2: $10.07 (201.4 bb)
MP3: $16.13 (322.6 bb)
CO: $10.25 (205 bb)

Pre-Flop: Hero is BB with Q K
UTG+1 folds, MP1 calls $0.05, MP2 folds, MP3 raises to $0.30, CO folds, BTN calls $0.30, SB calls $0.28, Hero calls $0.25, MP1 calls $0.25

Flop: ($1.50) Q 5 Q (5 players)
SB checks, Hero checks, MP1 checks, MP3 bets $0.25, BTN folds, SB calls $0.25, Hero calls $0.25, MP1 folds

Turn: ($2.25) 2 (3 players)
SB checks, Hero checks, MP3 bets $0.45, SB calls $0.45, Hero calls $0.45

River: ($3.60) 6 (3 players)
SB checks, Hero checks, MP3 bets $3.55, SB folds, Hero ??

Flat ? Shove ? Notice the ultra deep stacks.
Are we splitting this pot ? Thoughts on my play so far ?

Its a hard fold, but based off what you said your read is AQ is a possibility. Than again so is QJ, i would flat with 2:1 pot odds.

What about a river reraise ?