There are a few things to consider when answering this question. Is this month's bill the only one that's owed? Is the 15th the normal due date, or a payment arrangement date? If there is no past due balance and the 15th is the normal due date, then no, your service won't be shut off before the 19th.
If a customer has been on time for most of their payments and this payment will only be a few days late, typically this won't result in a shutoff. Do keep in mind, if a customer pays his/her bill late, even by a day, this may result in a late fee. If a late fee is applied it will show on their next bill.