Lets make sure your iPhone service is completely switched to your new iPhone 5s! Was this a brand new line of service that was opened or were you keeping the same number but putting a new phone on it?
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If you're switching devices - be sure to log onto your Verizon account and follow the steps to switch. If the old device is to be returned to Verizon, or if you plan to sell it, you'll need to log onto your iCloud account and remove the device from your account so that it can be reactivated in the future. Then turn the Find My Phone feature OFF on the phone before erasing all content and data. You can find specific instructions by logging onto your iCloud account.
Because the iPhone 4S is a CDMA 3G only smartphone, it will retain the phone number in the settings even if a different phone has been activated on that line.
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