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Q1: Which one is correct?

We executed two experiments over 5 weeks time span

OR,

We executed two experiments over 5 week time span

Q2: is it ok to write time span as two words?

Q3: is it ok to write 5 weeks or 5 week as two words?

2

I hope someone comes up with a more authoritative source, but to my understanding, neither is quite correct.

You'd want to use

We executed two experiments over a 5-week time span.

or

We executed two experiments over a time span of 5 weeks.

or even

We executed two experiments over 5 weeks.

Q2: sure.

Q3: "5 weeks" is two words, "5-week" as an adjective is one word.

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