Can I use the USB to wall adapter of an old iPhone for the iPhone 5?

I have an old USB adapter which allowed me to charge my old iPhone 3gs with my USB cable through the mains. I just bought a second hand iPhone 5 and I didn't get the wall adapter with it. Can I use the wall adapter from the 3gs with the iPhone 5's lighting port cable thingy?

Should be fine as long it is an original Apple USB adapter… Maybe.
Though I would suggest better to invest a new one since there's a length difference from 3gs to 5.