I think we would need a few more details. If you are applying now and your wife has been in Italy for just 5 months then no, you would not need to submit a PCC.
However, if she stays in Italy for more than 6 months, she would need to send an updated PCC later in the application process. Either when the VO asks for it or after your wife completes 6 months there (The VO may again ask for the same later on as well).
If your wife is doing a course through distance education and only needed to spend 5 months in Italy, then it would be a good idea to send the VO a cover letter explaining the situation. In this case, they may or may not request a PCC.
I hope this helps.
Wenstumped, you are really helpful, thank you. The issue is that my wife has already completed the course. It was a mobility course, which consisted of moving in different countries and the longest place she stayed was Italy, for 5 months. The problem is that, the papers of the course that she attended as well as the degree she received at the end, state that it was a course of 2 years long. Now, my concern is whether this might affect the problem of requiring a PCC from Italy (as the coordinating country of the course was Italy). So, the fact that the papers state the length of 2 years and actually she spent only 5 months in Italy. How can we prove it? By sending the copy of all pages of her old passport (just an idea)

Besides, there is smth that I'm still uncleared of: can it happen that VO asks for a PCC for any dependant at a later stage? Or it is fatal if it is not sent along with the application at first (even though it's abotu the dependant)?
Rgrds,
albabeu