The scene you describe is a very meticulous search, so #s 1, 2 and 3 are wrong: they suggest only a superficial search. #4's verb is right, but it does not collocate well with 'around'; 'They are exploring' is fine. #5 is reasonably appropriate for your situation.
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Mister MicawberThe scene you describe is a very meticulous search, so #s 1, 2 and 3 are wrong: they suggest only a superficial search.#4's verb is right, but it does not collocate well with 'around'; 'They are exploring' is fine.#5 is reasonably appropriate for your situation.However, 'around' does not lend itself well here in general. I would use something like this:They
Mister MicawberI suppose so, though I don't think that 'environment' is a very good choice.How can we explain the situation, if somebody is looking for a home for renting or for friends or for owning street cats?
Mr. TomI'm looking for an efficiency.This is not used by or familiar to all English speakers.