I had a Crown Vic that did a similar thing after the intake manifold cracked and somehow let coolant near the plugs and coil packs.
If the engine has coil packs, then i would suggest simply replacing the one on cylinder 5. They are probably less than $50 at autozone and should be a relatively easy swap if it is anything like my Crown Vic was.
I am not sure if AZ would let you return a coilpack if it turns out not to help, but they might.
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Current: 2007 335i sedan
Alpine White | Sports | Premium | Cold | Comfort Access
FORMERLY: 128i coupe
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