Easiest way to display 10 colours in a small area
Why don't you draw the colors on a piece of cardboard or similar material and use the LEDs to indicate which color is needed.  You only need to show the first 3 bands since they are for the resistor value, the others are for tolerance and reliability. Thus you would probably need a total of 30 leds, 10 for each of the first 3 bands.  But the LEDs could be  cheap red ones since they are only being used as indicators. If you want them to occupy a small area, place them in a circular pattern.