With one Cat5 you are more than covered. The easiest solution which I have used many times is to split out the Cat5 like eastside mentioned.

For 10/100 ethernet you only need two pairs from the Cat5, specifically the green and orange pair. It doesn't matter if you use 568 A or B for your termination because the green and orange pair are still in the same spot for each, just reversed. Once in a while I have even seen pre-made jumpers with this configuration if they were only going to be used in a 10/100 situation.

Your termination should be like this

----one---two---three------four--five---six---seven-eight
W/Green Green W/Orange Blank Blank Orange Blank Blank

Plug that part of the Cat5 in to your router/switch, and then the other end in to the ethernet on the RK3/4.

As for your remaining 4 wires, use them to transfer power from your power supply to the phoenix connector on the back of the keypad. If you don't double up your wires you'll even have two to spare.

As long as your keypads and processor are plugged into the same network, you're golden, and you can update the programming without running all over the house.