I do not believe ND references 5 years, but I know that some do; the Mountain West Conference LOI paperwork that I've seen reference 5 years, but that could be because there is some difficulty in graduating in 4 years (or there was in the past) due to difficulty getting certain classes, etc.
This also does depend on sport; I'm referencing football here. I believe other sports are more "annually renewable" due to scholarship limits/restrictions/etc.
There is a difference between a coach asking a guy to preserve the fifth year of eligibility and a guy having a fifth year of eligibility because he wasn't good enough to play as a freshman.
I've seen the former situation several times with ND basketball including this season. Sophomore JR Konieczny agreed to sit out this year because there are several upperclassmen of similar size playing the same position he does. As far as I'm concerned, JR should get the fifth year unless there is some kind of a disciplinary issue (which I don't expect).
That's a little different from someone like Matt Zona, who hasn't been ready to contribute at a major conference program, being guaranteed a fifth year even though he has the eligibility remaining.
Side note... Konieczny is a very athletic wing. I suspect he would have been better than at least two if the upperclassmen who were theoretically going to limit his playing time this season.