Brother HL-5470DW
Thanks.
That is an Apple AirPrint-enabled printer. Please read Connect an AirPrint printer to a Wi-Fi network - Apple Support. No drivers are required and no cable needs to be connected to it. If there is anything other than a power cord connected to your printer, disconnect it.
As far as macOS is concerned, a printer connected with a USB cable and that same printer connected wirelessly might as well be two separate printers. Since you do not need a cable for your printer, use AirPrint. Set the USB cable aside or throw it away. You don't need it.
If you still can't get it to work, I suggest "resetting the printing system" according to Reset the printing system, followed by adding that printer again as an AirPrint device:Connect an AirPrint printer to a Wi-Fi network.
Sometimes, you have to restart your wireless router or access point for an AirPrint-enabled device to be recognized on your Mac. To do that just unplug your router from the power receptacle, wait a moment or two, and then plug it back in. Be advised that all Apple routers are AirPrint-compatible (obviously) but all recent model non-Apple routers should be. You may need to update their firmware for that feature to work. Research your model router's documentation or support website.
If you're still having trouble, please review the suggestions in Resolve printer issues on your Mac - Apple Support.