I completed my last semester of college in 2021 and graduated in May 2021. Would still count as 5 months?

Yes.  Even if there were no classes in May, the fact that graduation was in May counts. 

Yes to be considered a student for the year, attending school in any part of any 5 months meets that time criteria.  Here is an extract from IRS Publication 501. 

Student defined.

To qualify as a student, your child must be, during some part of each of any 5 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 5 calendar months don't have to be consecutive.

Full-time student.

A full-time student is a student who is enrolled for the number of hours or courses the school considers to be full-time attendance.