My daughter went to grad school in August 2022 (08/2022 - 12/202s) her course load is full-time, but it is less than 5 month, does she count as a full-time student?

August to December is 5 months even if she was full time for only one day of each month.

However, if she is age 24 or older her full time student status is no longer relevant.  She can only be claimed as a dependent under the Qualifying Relative rules.

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,400 (social security does not count) in 2022
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.

If she was enrolled from August through December, attending full-time for some part of all five months, she would qualify for 2022. 

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.

This information is found in the Personal Exemptions and Dependents chapter of Publication 17.

Q.  My daughter went to grad school in August 2022 (08/2022 - 12/2022) her course load is full-time, but it is less than 5 full  months. Does she count as a full-time student, for purposes of the Qualifying child dependent rule?

A.  Yes. The rule is part of 5 calendar months.  So, being enrolled from 8/31/22 (or earlier) to 12/1/22 (or later) meets the 5 month rule.