Does it show a heartbeat on the front LEDs? If not,try flashing the SD,again. First I wrote the image as downloaded on SD card (raw mode). That didn't work nor did Etcher give me a negative feedback.Using the windows tool Mini Tool@Partition Wizard you can see if there are several volumes on the sd card.If not,you're doing it wrong. Never had any issues with Allwinner,Broadcom,Rockchip... Also I noticed I have to connect the WAN port and not LAN. Else you won't get proper access via DHCP.
Which image did you use? On the Nanopi R5C wiki there's a downloadlink to a gdrive.