Eid ul-Fitr

Culture/religion: Islamic
Date: May 2
Eid-ul-Fitr marks the end of Ramadan, the holiest month in the Islamic calendar, and traditionally lasts for three days. The celebration is a time of charitable giving, focused and careful prayer and a season of month-long fasting during daylight hours.
Greetings: Eid Mubarak (Blessed Eid); Eid sa’id (Happy Eid)
Sources:
Eid-ul-Fitr and Eid-ul-Adha – What is the difference?, Muslim Aid
Cinco de Mayo

Culture/religion: Mexican heritage
Date: May 5
Cinco de Mayo, Spanish for “Fifth of May,” is celebrated annually on May 5 to commemorate the Mexican Army’s victory over the French Empire at the Battle of Puebla on May 5, 1862.
The date is more popularly celebrated in the United States than in Mexico and has become associated with the celebration of Mexican-American culture – beginning in California in 1863. In Mexico, the commemoration of the battle continues to be mostly ceremonial with military parades or battle reenactments. The city of Puebla marks the event with an arts festival, a festival of local cuisine and reenactments of the battle.
(Not to be confused with Mexican Independence Day, which occurs on September 16.)
Sources:
Cinco de Mayo, Wikipedia