Can I run CAT5 cables parallel to low voltage (9v) power cables?
There's a decent probability that this won't work due to voltage drop from the power adapter, and not through interference:
Voltage Drop Calculator

A 15m run using 22AWG wires yields a voltage of 8 at the range extender. This may or may not be sufficient to power the extender.  

Power over Ethernet devices typically use 48v to minimize the voltage drop.

Alternatively, you could use a wifi access point with a powerline ethernet adapter;  I've used this setup with great success.