Deductions & credits

No, reporting it will only result in subtracting the grant from the education expenses, NOT making the grant taxable. It is limiting the expenses you can use towards an education credit.

According to the IRS:

“Q2: I received an emergency financial aid grant under the CARES Act and used some of it to pay for course materials that are now required for online learning because my college or university campus is closed. Can I claim a tuition and fees deduction for the cost of these materials, or treat the cost of these materials as a qualifying education expense for purposes of claiming the American Opportunity Credit or the Lifetime Learning Credit?

A2: No. Because the emergency financial aid grant is not includible in your gross income, you cannot claim any deduction or credit for expenses paid with the grant including the tuition and fees deduction, the American Opportunity Credit, or the Lifetime Learning Credit. See section 139(h) of the Internal Revenue Code.”

IRS Source

Yes, if you were not considered a full-time student for those 5 months, you would not be their dependent. I understood you as meaning that it was part-time since it was only part of the year. To clarify, I included the TurboTax link with more information. I felt your real question had to do with the HEERF Grant. Now that I realize you were only part-time for those 5 months, you are correct. 

For being a dependent: 

"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."