If you run the ipconfig/all in a Windows command prompt, does it show the DNS server as the Slate AX IP address 10.0.5.1? If so, then the DNS request is first sent to the router, which then forwards it to the AdGuard Home IP address 10.0.5.5. Hence, AdGuard Home would think the request is from the router.
In this situation, you can set the DHCP server to give out 10.0.5.5 as the DNS server to the clients. so DNS requests go directly to AdGuard Home.
I do not work for and I do not have formal association with GL.iNet
I agree that you should set up at least 2 Upstream DNS servers in AdGuard Home, which could be CloudFlare.'s primary DNS 220.127.116.11 and secondary DNS 18.104.22.168. On my AdGuard Home, I use DNS over HTTPS.
I also set up 2 separate AdGuard Home servers, in case one goes down due to problems or for maintenance. My primary AdGuard Home server runs in Docker on Synology NAS that is very reliable and my secondary AdGuard Home server runs on a standalone GL-MV1000W BrumeW that is connected via Ethernet LAN port only, without any WAN.
All I had to do to was to set up the DHCP server on my main router give out the 2 IP addresses as the DNS servers to clients. On GL.iNet/OpenWRT routers, you have to do that with a DHCP Option via LuCI → Network → Interfaces → LAN → Edit → DHCP Server → Advanced Settings → DHCP-Options.
I believe that would be the DNS server for the Slate AX router (LAN interface) itself, not given out to client devices. To check, you can run the ipconfig/all in a Windows command prompt on a client device to show it DNS Servers.
The DHCP Option can be entered in the DHCP Server tab.