In theory, you can. It is possible, Cat5 is just 8 pieces of copper. However. You have to take care of the ground loops. Different electrical outlets can be on different phases. Also, even in static configuration, the system might work, it might take one lightning hundreds of meters away to kill it. We are talking about 1Km cable. Capacitive loading will be a problem. There might be even reflections.
It is possible, but I think it needs more consideration than soldering the datasheet example it on breadboard and good to go.