Does the iphone 5s use the same exact charger as iphone 5?

My dad bought me a "Apple 8-Pin Lightning USB Cable" from discount electronics cause he knew my charger was breaking, but it says "for iphone 5s, ipod touch 5g, ipod nano 7g. IOS7 compatible." and I have the regular iphone 5. The package is made to where I can't see the end of the charger that plugs into the phone anyway. Can I use this for my iphone 5? Once you open the package you can't return it.

Yes, the iPhone 5, 5c, 5s, 6, and 6Plus all use the lightning cable. However you may run into the issue where the phone rejects n aftermarket charger. More information in the link below.
Chances are, if its a decent lightning cable you'll have no problems!

http://www.phonearena.com/news/Apple-blocks-unauthorized-Lightning-cables-with-iOS-7_id47612

It is fine but be aware that with third party parts it may or may not be reliable. ONLY Apple accessories will work with no problems.

Post a picture of the package

Yes they do, but as was mentioned if you got some aftermarket charger cable there's a possibility that either it will not work for syncing purposes (hold the connection long) or the iPhone would reject from the get go.