How to disable the "this cable or accessory is not certified" message on iPhone?
So iPhone 5s use a Lightning cable rather than the old school dock connector. 

Lightning cables actually have an authentication chip in them, hence the message.

There's a jailbreak tweak out there that may be worth checking out, but it's quite old and may not have been updated.

Your best bet would be to just get a new cable. Certified cables can be had for $8 on Amazon, and you don't run any risks of having dodgy cable damage your phone.

It's not just Apple protecting their profits, either. Certification actually means standards were followed.