The SLC-5/05 controller can ONLY communicate over Ethernet using A-B proprietary protocols.
It cannot "just open up a socket" or transport ASCII over Ethernet. Unless your barcode reader supports the A-B PCCC protocol or PCCC Encapsulation in EtherNet/IP protocol, you absolutely cannot use it with the SLC-5/05's Ethernet port. I haven't seen any barcode readers that do so, although probably MicroScan's MS880 is the best candidate.
If all you need is one barcode reader inputting to the SLC, go ahead and use the Channel 0 RS232 port in ASCII mode. If you don't want to give up the ability to use Channel 0 to program the SLC, get a Tomantron MUXIPort device.
If you need more than one barcode reader, or need a lot of parsing ability, consider a BASIC or C-programmable coprocessor module.
My favorite way to get barcode data into SLCs is via DeviceNet/ASCII converters like the 1734-ASC2 or WRC's 1782-JDC, but then virtually all of my SLC systems use DeviceNet I/O.