Yes either cat 5 or cat 6 will be fine, but you will need to make sure that you manually set the IP address and subnet masks of each of the devices correctly.
For example, you could set the address of one of the devices as 192.168.1.1 with a subnet mask of 255.255.255.0 and the other device as 192.168.1.2 also with a subnet mask of 255.255.255.0.
They should then be able to communicate with each other by IP address across the Ethernet cable…
Let’s assume that you have a computer on 192.168.1.1 running Jriver and the dac is configured to use 192.168.1.2.
You could then stream music from Jriver by using the JRiver user interface on the PC to tell jriver to play files from your library on the direct stream dac which should show up as a device called Bridge II by default.
Keep in mind that you won’t be able to use the mcontrol software on your mobile device to control what plays because there is no way for your mobile device to communicate on the private network running over the wire between the two devices.