Pushing 50W over PoE?
Yes you can deliver 50W over a cat 5 cable, the POE standard supports this:


Source: IEEE 802 3bt DTE Power via MDI over 4 pair task force

There are two ways to do this:



Source: Infocellular

So you would want to use the first method, with a step up DC/DC converter to boost the voltage to 48V. On the device end you can use your step down DC\DC's. The voltage is boosted to cut back on resistive losses in the cable. There are transformers that block DC on ethernet devices so your probably not going to get into too much trouble if you mix things up.

If you want it to be compatible with standards, then you will want to use the appropriate detection circuits. Usually POE uses rectifiers on the device end so either AC or DC can be used, but you also have a diode drop. If your running your own custom solution and pay attention to polarity then you would not need this.