This is a line I've started taking much more often live. Donking the turn, bombing the river. The donk usually comes when I pick up equity on the turn or when I believe pre-flop raiser can be capped. Also very opponent-dependent.
It is actually INSANE how often it works, because this spot is severely underbluffed, especially when the bdfd doesn't actually come in.
Let's assign some suits to OP's example:
Hero A
J
Villain 4
5
Board A
J
5
2
Q
Now if I'm villain...overlimp/call pre with 4s5s is questionable but not awful. Flop call is fine. Now...lead turn when you pick up a gutshot and fd with the intention of following through on (nearly) all rivers. Hero is somewhat capped here (has very few flushes and K10). Puts hero in a tough spot.
It's a great play because you should be well balanced as well, because you'll also be leading turn for value some % of the time, and you'll also get there on the river some % as well.
Not saying villain in OP is doing this...in fact almost no one is...but it's something I've had good results with