First thing to try is to temporarily disable all WiFi security. Make it an open hotspot and see if your Realtek dongle can connect. Some devices refuse when they see a network with security settings they don't recognize. (For security you should only be using WPA2 + AES. No WEP, no WPA (without the 2), no TKIP. If any of your devices does not support WPA2 + AES, throw it away and replace it.)
The other thing to watch out for is that the 5 GHz band is a bit fragmented. After the band was opened, they discovered that the frequencies right in the middle of it were very useful for a certain type of doppler weather radar. Many airports (mostly in the U.S.) use that radar, so regulatory agencies had to go back and put new restrictions on how the 5 GHz frequencies are used. The channels which overlap weather radar are now labeled DFS (dynamic frequency selection). Devices can use them, but must vacate them (dynamically switch to a different frequency) if they detect weather radar is in use.
Most WiFi device manufacturers didn't bother, and simply blocked out the 5 GHz channels which are DFS (channels 50-144 in the U.S.). If your WiFi adapter is one of these but the WiFi router is not, the router can end up using a DFS channel that the adapter cannot see. You'll have to go into the router settings and manually set the 5 GHz channel to something between 36-48, or 149-165. (That's for the U.S. Check the chart below if you're in another country.)
https://en.wikipedia.org/wiki/List_of_WLAN_channels#5_GHz_(802.11a/h/j/n/ac/ax)
And no, the wireless frequency doesn't matter for Ethernet.