If I started school I was in school from end of Aug- end of Dec does it count as 5 months of school?

Each school defines "full time" in its own way (usually in terms of the number of courses or hours). 

According to the IRS, a full-time student is defined as a student who is enrolled for the number of hours or courses that the school considers to be full-time attendance. 

To qualify as a student, you must be (during some part of each of any five calendar months of the year):

1. A full-time student at a school that has a regular teaching staff, course of study, and a regularly enrolled student body at the school, or
2. A student taking a full-time, on-farm training course given by a school described in (1), or by a state, county, or local government agency.

For more information, please check: Am I considered a full-time student?

Q. Does it count as 5 months of school?

A. Yes.  Any part of a month counts.

Q. Do I qualify as a full time student?

A. That depends on the school's credit-hour requirement for full time.