What if I just connect 5V DC to my UTP?
Not exactly. That RJ45 connector labeled HR911105A is internally connected like this:


It's possible with PoE version (but I suppose not with 5V but more like 12V or so)

Or there are variants without PoE module connected but with support, that should be possible to use 5V if you wire it correctly)

Or you can use external PoE injector and extractor: 

For 100Mb networks are two unused communication pairs used as power lines: