All five of the sentences are pretty bad, to tell you the truth, though (5) is technically correct. The problem with (2) is that "put" wants to be "fit":
(2a) This chair can fold to fit in the trunk of a car.
I suppose the correctness of (1) is debatable. I don't like it, though. I suggest that its sentence-ending infinitival be changed to a passive "if"-clause:
(1a) That letter needs to be read at least twice if information is to be extracted from it.