Partial Exception to Five-Year Rule for People Granted Asylum (Asylees)
If you got your green card based on having received asylum in the United States, one year of your time as an asylee counts as if you were a permanent resident (known as "rollback").
Note, however, that if you waited longer than one year after receiving asylum to apply for your green card, that extra time will not be counted toward your permanent residency period. You will have to wait a full four years from the actual date when you're approved for a green card.
And, somewhat confusingly, you will need to wait a full five years from the date your green card says you became a permanent resident. That's because USCIS will automatically backdate your permanent residence approval date on your green card by one year, in recognition of your rollback rights.