I assume you mean the SLC was 1747-ASB (Remote I/O Adaptor Module), I am not familar with a 1747-RIO card. I assume you are intending to say the 1747 is using RIO?
You will need to have a 1756-DHRIO or 1756-RIO card to maintain the usage of the RIO adaptor on the SLC chassis. If you have analog IO on the rack, the PLC5 used BTR/BTW (Block Transfer Read/Write) instructions to send data to/from the analog cards. Logix does not use these native instructions, you need to convert these to MSG instructions and configure them maually.
I would recommend ditching the 1747-ASB for a 1747-AENTR to put it on Ethernet which would things much easier, however there are limitations to the 1747-AENTR so read the manual. Also ensure you can actually run Ethernet. If you are stuck with RIO, then you need to read the 1747-ASB manual, the 1756-DHRIO manual, the PLC5-Logix Transition tool manual, and would be helpful to read up on the PLC5 manual to understand BTW/BTR instructions and what is happening.
RIO requires setting dip-switches for addressing, and is crucial to understand.
Not an easy topic, do plenty of reading and comeback with specific questions. s