Will i qualify as a student if i started the semester in January of 2021 and graduated May of 2021?

Yes----if you were a student for any part of five months in 2021 you can be called a student.  

  Are you and your parents trying to figure out if they can claim you or if you can say you cannot be claimed as a dependent?

It gets tricky for the year of graduation so provide some details if that is an issue.

Yes, you will qualify as a student if you started the semester in January and graduated in May.

Per the IRS, "To qualify as a student, the person must be, during some part of each of any five calendar months of the year".

If you graduated on May 1st, then the entire month of May counts as one of your five months and since you started in January and graduated in May, this will count as 5 months.

The 5 month (full time student) rule comes into play in determining whether you can be a "Qualifying Child" dependent  of your parent(s). 

There is no 5 month rule for claiming an education credit. So, for example, a student on the quarter system, graduating in March could still claim a credit or deduction.

Can you parents claim you if you graduate in May?

Graduation year (written as if the parent asked the question)

If he/she was a student (under 24) for at least 5 months and lived with you for more than half the year, and did not provide more than 1/2 his own support for the whole year, you can still claim him. Be sure he knows you're claiming him, so he doesn't claim himself. He can only be claimed once. But, he can "file taxes" without claiming his own exemption.

The real question is who should be claiming him in this "transition" year to adulthood. You two have to agree on who is going to claim his exemption. Each should do their taxes both ways and see which way the family comes out best.  Even then, you have to meet the rules. The rule is that a child of a taxpayer can still be a “Qualifying Child” dependent, regardless of  his income, if:

1. he is a full time student under 24 for at least 5 calendar months of the year (graduating in May usually means you meet the 5 month rule)
2. he did not provide more than 1/2 his own support  (scholarships are considered 3rd party support and not support provided by the student). 
3. lived with the parent (including time away at school) for more than half the year

So, it usually hinges on  "Did he provide more than 1/2 his own support in 2020.

The support value of the home you provided is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants. IRS Publication 501 on page 20 has a worksheet that can be used to help with the support calculation. See: http://www.irs.gov/pub/irs-pdf/p501.pdf  (page 15)

If he has already filed one way, he can file an amended return, going the other way.