If you really have a 5, then you can't use the fingerprint sensor, because you don't have a fingerprint sensor. That was a new feature of the 5s, older iPhones don't have a fingerprint sensor.
If you somehow got a used 5 upgraded with a sensor (I don't that's possible, but... ) and the sensor suddenly stopped working properly, you can try an iPhone Restore from iTunes. That will reset certain parts of your hardware, and clear out any fingerprint data, which you can then re-enter when you begin using your iPhone.
If it still doesn't work (and I can't think of any reason that it would), then you can make it function by replacing your iP5 with an iP5s, or a 6 or other newer model.