If we knew that the probability that an order was processed on the same day was independent of the number of orders recieved on the day it was recieved, or the number already processed. Then or 500 orders recieved under the null hypotheseis that 95% are processed then we can construct a test based on the assumption that the number of these processed on thesame day ~B(500,0.95).

However the assumptions are inplausible, and without further knowlege or a better model of the order processing system no sensible answer can be given.

RonL