Some phrasal verbs

Sorry, I’ve kept studying the phrasal verbs these couple days.
Sometimes, it’s really confusing.

Q1: I turned the lights out before leaving.
“turn out a light” and “turn off a light” are the same?

Q2: Sometimes it works out cheaper to eat in a restaurant than to cook at home.
Is it okay to use “turns out” cheaper instead of “works out” in this sentence?

Q3: They got married a few years ago but it didn’t work out, and they separated.
It didn’t “work out” here means it didn’t succeed?

Q4: A: What happened about your problem with your bank?
B: It’s OK now. I went to see them and we sorted it out.
Can I use “worked it out” instead of “sorted out” here?

Q5: “sort out” a mess means to organize or arrange a mess?

Thank you!!!

Q1: Yes.
Q2: I prefer ‘works out’, but yes.
Q3: Yes.
Q4: It depends. To me, in this case, ‘worked it out’ means there was some sort of problem and now it’s solved, while ‘sorted it out’ could mean that there was just some misunderstanding and not a real problem.
Q5: No, it means to fix/resolve it.

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Q1 yes they are the same
Q2 “works out cheaper” is better here. You could say “turns out to be cheaper” but it doesn’t sound as natural.
Q3 yes you are correct ‘didn’t work out’ means it didn’t succeed in this sentence.
Q4 yes you could use ‘worked it out’
Q5 ‘sort out a mess’ normally means to fix a problem that someone has created. “He made a mess of the job and I sorted it out”. You could also 'tidy up a mess" or “clean up a mess” " My young son made a mess in his room and I cleaned/tidied it up" but you wouldn’t organise or arrange a mess.

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