You might also consider something like the Netgear Powerline Ethernet adapters:
https://www.amazon.com/dp/B00S6DBGJM/#_swftext_Swf
Plug one unit into a outlet next to the router with a short ethernet cable between the two, the other at the Entertainment center destination with the outgoing ethernet going to the TV/Roku. We have something similar setup at our house that's not CAT-5 wired and seems to work fine.
Edit: Did a bit more research and these might not work with RV's wired with GFI's. So all you could do is give it shot, and if it doesn't work, take them back.