Measure alternating voltage with arduino
A simple voltage divider, but used backwards, would solve your problem.



Link to simulation.

If you click the link above, then move the mouse over the -5V and scroll with your mouse button. It will change the input voltage and you will see how Vout changes accordingly. Or look to the right of the screen, where it says "Voltage" and move the slider. 

Important things:


The resistors must have the same value if you want to map [-5,5] => [0,5] Volt
The middle point is the output
One of the resistors goes to 5 V
The input goes to the other resistor


I've chosen 1 kΩ for both of the resistors. This is a good value as it is not too small or too big. It is "Lagom", as we say in Sweden.