I'm not too crazy about the preflop call, but its close. Since no one folds to 3-bets at $5NL, calling & folding are probably your best two options.
Once villain checks back the turn, his range decreases in strength pretty significantly. It comprises mostly air, weak draws, and hands like second pair. Thus, it just becomes a question of his tendencies and the board.
Since all the draws missed, this is a pretty good spot to check and induce a bluff since villain may have some of those draws. Since most of his range is air, and draws that bricked, I'd let him fire again.
But of course, if he's really stationy, or he reads hands somewhat well, I'd be tempted to bet half pot on the river. My standard line though is to just check here to your standard loose-bad $5 NL villain who has put himself in a steal situation. He's made a play at the pot preflop & on the flop, and that can often put people in a stealing mindset.