If you have an older 30 pin cable you can get lightning adapters for them. There are two that are available from Apple:
This one is the cheaper of the two but it has the disadvantage of not working if your iPhone is in a case. The added thickness of the case keeps the contacts of the connector in making contact with the connections in the receptacle.
This adapter works even if your phone is in a case or not. Of course it's going to cost a little more than the precious one, but it's worth it.
Another possibility is getting a Belkin lightning cable:
They work great and I haven't had any issues with them.
I recently bought the 3rd party braided cables off of ebay they are much cheaper and you have to really abuse them to break that connection between the cable and lightning connector
Using the same iPad wall adapter, some aftermarket lightning cable will charge a 5s, but won't charge an iPad Air.
I've had the best compatibility lightning power/data cords made/sold by amazon. They are called "Amazon Basics". The Amazon Basic cables are the only aftermarket cables that will charge my iPad Air.
Of course there are 100's of different aftermarket cables and other may work perfectly fine along with the Amazon Basics cables. (And of course the OEM cables).