Definitely not normal to take 5 minutes - we’d normally expect around 30 seconds from power on for companion to boot successfully, at which point QGC should display the camera feed and start connecting to the pixhawk, and the web interface should be available. It’s best to open a new browser tab when connecting to the web interface.
I’m currently doing a relatively in-depth review of our documentation to identify missing or outdated information, and working on adding to and fixing that to improve the user and developer experiences - this is useful feedback. Some of the physical status indicators are documented (e.g. beeps for ESC connections and valid input/stopped signal in the Basic ESC learn tab), but I agree that it’s somewhat fragmented and could be made clearer with a more detailed walkthrough of a ‘normal startup’ or similar.
I expect that historically the various status LEDs of the Pixhawk and Raspberry Pi haven’t been in our documentation partly because they’re external products that have their own documentation, but perhaps mainly because the issues people tend to have most frequently aren’t indicated by those LEDs. From what I’ve seen so far the issues are more likely related to incorrect device connections or software settings, which can only really be debugged by connecting to the companion computer (via the web interface or ssh), or checking computer network settings and firewalls and the like.
That’s not to say the LEDs and their meanings aren’t useful though - they play a part within the larger task of making sure things are working as expected. I’m thinking a walkthrough of standard checks could include both physical and software-based indicators, and possibly include links or collapsible sections describing how to detect and fix abnormal behaviour.