STM32f0 Low power mode
I guess you are measuring the quiescent current of the voltage regulator on top of the MCU stop current.

If this schematic is the correct one, there is a LM1117-3.3 voltage regulator on board.

The datasheet for the LM1117 shows a typical quiescent current of 5mA.

So you have a typical 5mA plus a typical 500µA which results in a typical 5.5mA. Pretty close to what you are measuring.

Maybe you can try to just measure the difference between active and stop current and see if that difference corresponds to the difference calculated from values in the datasheet.

EDIT1:

I'd also suggest to perform SystemClock_Config() at the start of the program and not at the end of the while() loop. The content of the registers is preserved during stop of the controller.

I must say that I am a bit curious what a microcontroller is supposed to do when it is not connected to anything.

EDIT2:

I was thinking that the debugger/programmer might interfere with your measurement, but if you disconnect the SWDIO and SWCLK line and reset the controller it should be fine. The debugger can enable some internal debugging peripherals which might consume additional current. Resetting or power cycling will reset those peripherals, so they are inactive.

At this point I am at a loss what might cause this current draw. Just another idea: check that there are no solder connections where they shouldn't be. I managed several times to create a solder bridge which was small enough to not be a short circuit but strong enough to cause a significant current flow.