Gareth,

You should be able to use the same Cat5 wire. As long as the protocol used on the serial box is TCP/IP you can connect the two of them. Each device can be assigned to a different subnet if you require separation. However, you shouldn't really need to separate the nodes.

One issue you'll face is the ability to run both devices. Ethernet does not daisy chain. You would still be required to have a switch (technically just a hub would be fine) at the projector to send a signal to each node. I'm inclined to believe that the extra ethernet cable is worth more than the extra switch in terms of cost savings and reliability.