+5V, GND and -5V from +12V DC power supply

I want to create an aquarium controller with an PH probe using an arduino.

For the ph amplificationcircuit i need +5V and -5V. how can i obtain this in the simpelest way possible?

I was wondering if i could use a 7810 and 7805 to generate 10V, 5V an 0V then by using 5V as ground this would render +5V, 0V and -5V.

Would this work or is this utter nonsense?

edit:
nvm, the 7810 datasheet states it needs at least 12.5v to operate...

what is a good solution for my problem?

what is the PH Probe you are using and what sort of connections does it need ?

I wanted to build this circuit:

using a generic ph probe from ebay:
http://www.ebay.com/itm/PH-Electrode-Probe-BNC-Connector-for-Aquarium-PH-Control-Controller-Meter-Sensor-/371009490734?pt=LH_DefaultDomain_0&hash=item5661e38f2e

deleenheir:
I was wondering if i could use a 7810 and 7805 to generate 10V, 5V an 0V then by using 5V as ground this would render +5V, 0V and -5V.

Would this work or is this utter nonsense?

It would work.

Doesn't it pose a problem when the power consumption between +10V and +5V are bigger then between +5V and 0V?

can the 7805 handle the access on the +5v rail?