I graduated from high school on May 24th 2022. Am I eligible to claim 5 month full time student status for this time period?

[xmasbaby0]

The questions about whether you were a full-time student are leading toward higher education credits ---so college tuition and college expenses.   The "student" questions are not about high school even though you were a high school student.  

[Hal_Al]

It depends on why you are asking the question.

The only thing this would be relevant for is: if you were 19 or older, in 2022, being a full time student for  months would help qualify you as a "Qualifying Child" dependent for 2022.  High school would count for that test.