Negative voltage from Arduino?
If you only need a few mA the simplest solution is to use a charge pump like the ICL7660 to create -5V from +5V:  

  

As you can see it only needs a few components. This simplicity has its price, and that's that the output voltage starts to drop if you load it with more than just a few mA.    

Alternatively you can use an inverting SMPS (Switch-Mode Power Supply), like this one 



which will allow for more current. The ratio R1/R2 sets the output voltage. This is the simplest switcher application I know. An SMPS however requires careful component selection and PCB layout to get a good efficiency and low EMI.