Electronic – Please help with resistor color code

It's 0.47\$\Omega\$. The black band is just to tell you which end is the right-hand one. Probably a 5% metal oxide film (flameproof) type that also acts as a fuse.

Chances are very good that something else has failed to cause this catastrophic failure- such as a MOSFET or high voltage transistor, so replacing that resistor will more than likely result in a repetition of the failure (correct type) or possibly more dramatic results (wrong type of resistor).

That resistor is toast for sure, but the spiral 'bump' indicates it is a wire-wound resistor of at least 1 watt. The first band is either red or orange, so if it is 0.33 ohms or 0.22 ohms that would make sense as a series current limiting or current sensing resistor. It may be so damaged that the nickle-chrome wire is no good, or its bond to the end caps has gone bad.

If you look at the top of the burnt resistor the nickle-chrome wire appears to be burnt away, creating a gap, so this resistor should measure as being 'open' or infinite resistance. It could also be in the category of "Fusible" resistor or at least "Flame proof".

If installing it as it is now causes problems I would try both a new 0.22 ohm 1 watt and a 0.33 ohm 1 watt to see which works best. The higher value is best as long as the motor runs at expected speed and torque. Note that this was a 1% tolerance resistor. Such a tight tolerance is normally used for accurate current sensing.