I'd call the turn. I don't think there's any harm here letting in weak-ish highs (two pair, even sets) as they're dead money to you, and I don't think there's any harm letting in anyone with a non-nut low. It seems a strong possibility that the guy who suddenly wakes up on the turn has at least the same low (likely with something for high), so ordinarily I wouldn't think that trying to engineer an all-in with him has much merit, although you could be solidly free-rolling him I guess. A raise wouldn't be terrible, especially if you think the guy who bets the turn is quite LAGgy (obv. getting it all in here against a naked high would be decent). I'd certainly never consider folding this turn and think that would be pretty abysmal.
However, I really don't see the merit in betting the flop, unless this table is outrageously bad. With 4 opponents seeing the flop, it's hard to believe someone doesn't have an A2 or A3 here; I guess if it's the sort of table where everyone sees every hand, you might be ahead on the low, but if not, you really need to see precisely an ace on the turn to be interested in the low end, and obviously still have to make your straight. I really don't think this is a bettable hand with 5 to the flop.