Solder a female 9-pin D-shell connector on the end of each cat-5 cable, with pairs as
1 2 3 4 x
1 2 3 4
Mount the three D connectors in a bracket to the side of your breadboard.
Use single pins from scrap male D-connectors, with solid-core wire soldered in, as flying jumpers from the pins of the mounted D connectors, to your breadboard.
This way you get the cat-5 cables solidly mounted, plus an easy and flexible patching system.