Can I claim the AOTC? I started college in fall of 2017 and graduated May of 2021.

The four years for AOTC are four academic years or claimed for years on taxes. 

To be eligible for AOTC, the student must: be pursuing a degree or other recognized education credential. Be enrolled at least half time for at least one academic period* beginning in the tax year. Not have finished the first four years of higher education at the beginning of the tax year.

If you are in a graduate program you cannot take AOTC but can file for Lifetime Learning Credit.

Based on the information provided it sounds like you are eligible to claim the AOTC.

AOTC

You, most likely,  qualify for the AOTC for 2021.

There are two 4 year rules.  The first one says you must not have completed four academic years before 1-1-21, Graduating in May 2021 means you met that rule.  Note that if you had started grad school  in the fall of 21, your grad school tuition would also qualify for the AOTC (because you had not completed 4 years of college by the beginning of the tax year).

The 2nd rule is that you (and/or your parents) may not claim the AOTC more than 4 times on your  education.  Since 4 academic years of college usually takes 5 calendar/tax years, it's possible that you don't meet this rule. So, if you (or you parents) had claimed the AOTC in 2017, 2018, 2019 and 2020, you would not be allowed it for 2021.