In a Bank Drive-Through, There Is a Single Service Window

Short Answer

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed.
-What is the probability that the system is full and new arrival must drive on?