The device's own summary is pretty odd: it seems to be using as large a bar for the 600 MB free as for the 5GB system! And it's not clear what it does with the data that don't fit into its few categories.
The Disk Analyzer display seems straightforward: it's showing a 10GB /data partition, which can also be addressed as /sdcard0, and a 2GB /system partition (which is where the Android OS and pre-installed apps live). There will be other partitions where other parts of the system firmware live (/boot, /recovery, the partitions where stuff like the radio firmware live, and possibly a system /cache partition, depending on what Android version this device runs). Chances are that these are lumped together into the 5GB system usage that the system settings show.
In reality a device with 16GB storage having 10GB available to the user is nothing unusual. And if the rest is system partitions there is nothing you can do about that: you'd need root to remove anything from those, and that wouldn't create any more space in the user partitions anyway so would not solve your problem.
So given that your partitions look plausible, the real question is whether there is anything in the user partition which wasn't cleared by your reset? Apart from the hassle of reloading everything I'd be tempted to try a factory reset (and make sure that it does clear the user storage rather than just apps) to see whether that fixes it.