5 There was no/any/many information about when the new shopping mall would open.

No is the correct answer.
Explanation: "Information" is an uncountable noun. To indicate that there was no information, "no" is used before the noun. While "any" can be used in questions or negative contexts, "no" is more direct and appropriate in this case. "Many" is for countable nouns, so it's not appropriate here.
Answer: no