Test the jack for a signal. Insert an ethernet loopback jack or sniffter into the jack. It will detect the Internet connection and give you a proper display light if

Most Powerline kits provide two adapters, each with an Ethernet port. One device connects to an electrical outlet and tethers to a modem or router’s LAN port using an Ethernet

RJ45 is the connector and CAT5 is the cable. They are not rival standards competing to do the same job. An RJ45 plug crimps onto the end of a CAT5