Documentation: Custom Quick Icons module
FontAwesome Icons 5
In Joomla 5 version of the Custom Quick Icons module you can select a FontAwesome version 6 icon with the modal iconpicker.
(When no icon is selected, the Joomla logo will be displayed as default)
Click on the "Select Icon" button.

Then a modal popup will open with all icons. (on top of the popup you can search for a specific icon and you can see which version of FontAwesome is used)

Click on an icon to select and close the popup.