What were five important events that happened in Gandhi's life?

I assume you mean Mahatma (there were also other relevant Gandhis: Indira, Sonia)

Some important events in his life were:

-his time in Jail in South Africa, which made him sensitive to racism

-his involvement in the Boar War when he was an ambulance driver

-1920 Gandhi took leadership of the Indian Congress Party

-his non-cooperation movement starting in 1921

-Indian independence in 1947