My college semester was mid-January through early-May. For the purposes of defining "full time student," do those count as a full 5 months?

Yes, this would be 5 months for the full time student requirement

According to IRS publication 17, a full-time student is 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, the person 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.

The five calendar months do not have to be consecutive.