You do not need to wait five years if you are a lawful permanent resident adult and you receive a disability-based benefit because of a severe disability. 106 C.M.R.§362.220 (B)(7)(e). This policy also applies to battered immigrants and humanitarian parolees. If you are under age 18, you do not need to get a disability-benefit and there is no 5-year wait.
How do I show DTA I am disabled? explains the disability rules for SNAP and multiple ways you can qualify as receiving a "disability based-benefit" including through EAEDC or MassHealth.