I'm not an HR professional, I don't even work in your field, but anyway: the cover letter is supposed to give a specific reason why you want to join this particular organisation in this particular role, and about what makes you think they should hire you for the job.

From that point of view and bearing in mind someone's going to have to read the letter (plus all the letters in all the other applications they received), 3-5 pages sounds ludicrous to me, I'd go for 1 page at the very most.