"Specified" student or unspecified have no meaning in income tax filing. The 5 month rule affects certain tax attributes, primarily whether you can be claimed as a dependent under the "Qualifying Child" rules which have no income limit.
The 5 month rule does not affect whether you qualify for the tuition credits.
So, the answer to you question, depends on why are you asking the question. That is what are you trying to do or claim. in taxes.
