Buying a new iPhone 5s

yes be cautious (and I assume it's not kosher according to Levitical law)

Without the receipt from the actual Apple Authorized Retailer you may have issues if you are locked out of the phone and are required by Apple to provide ownership because "Actually I got it from a company called _______" is not any answer Apple may not be able to do much more than suspect the device may have been stolen and in that event you may have just bought a brick.

Ebay, Amazon, Cragislist, etc: these are not Authorized Apple Retail Stores, they sell Apple products, they sell hood ornaments and ukulele strings too.

Any issue you have with this device will be entirely something you need to sort with that seller so whatever their policy is is what you are stuck with.

If you go ahead with this purchase you need the seller to provide you the receipt from the Apple Authorized Retailer this phone was originally purchased from, not from them, they are not an authorized retailer, their receipt is worthless. Without proof of ownership in the form of an actual receipt of the original transaction from the Apple Authorized Retailer Apple may be unable to assist in matters that arise with the phone.

If you buy a new phone from an Apple Authorized Retailer the warranty will be begin on the day of purchase, regardless if the box was opened or not.

if you buy a refurbished phone directly from Apple you will be given a warranty on the device. Note: refurbished devices from Apple Authorized Retailers are not covered by any warranty.

The warranty from Apple is only good in the same country your bought the cellular device from.