You are not required to pay the early withdrawal penalty at all. "Separation from service" means you left the job, whether by retirement, quitting, fired or laid off. The distribution (withdrawal) in 2016, from your previous employer's 401k, does qualify for the separation from service exception, to the early (before age 59-1/2) withdrawal penalty because you were 55 or over when you separated. There is no time limit for the withdrawal.
Had you rolled over the 401k to an IRA, any subsequent distribution from the IRA would not qualify (but might qualify for the home buyer exception). Home buying is not a penalty exception to a 401k distribution (only IRAs).
