We can say–
Five Important Tips to Bring Success to Your Business
But then, what about –
Five Important Tips that Bring Failure to Your Business
I was thinking of a title like this –
Five Important Factors that Contribute to your Business Failure
OR
Five Important Hazardous Factors that can Make You Sick for More than a Month
Whenever we utter the word 'important', we get a positive vibe drawing our attention. Said that, 'important tips' have to be positive. Is it possible to use it in a negative way?
I'm not asking about using the words – 'unimportant' or 'not-important'.
Best Answer
Your examples give titles, not sentences. The exigencies of title-writing are different from those of sentence-writing.
Five Important Things that Can Cause a Business to Fail is grammatical but the title would be better without "important".
"Important" means "having significance" and, by extension, "warranting attention" or "to consider" or "to be considered".
So, in these titles:
Five Things Warranting Attention that Can Cause a Business to Fail.
Five Things to Consider that Can Cause a Business to Fail.
"warranting attention" and "to consider" are otiose.
P.S. I will also go out on a limb here and say that "important", just like "warranting attention", creates a virtual restrictive clause that clashes with the actual restrictive clause in the title.