Why is there no such thing as a 475 ohm resistor, unless you are looking for a precision resistor?
The simple answer is because resistors are not perfect. They have a tolerance, which means a given resistor will have a value that is its stated value, plus or minus a percentage. Common, low cost, resistors may have a tolerance of either 5% (the fourth colour band is gold) or 10% (the fourth colour band is silver).
Consider resistors with a 10% tolerance. If you start with a value of 100 ohms, then a given resistor with colour bands of brown-black-black-silver could have an actual resistance as low as 90 ohms or as high as 110 ohms. This makes it unnecessary to manufacture specific resistors in this range. The next value available in the 10% series is 120 ohms, but resistors with colour bands of brown-red-black-silver may have an actual resistance as low as 108 ohms or as high as 132 ohms.
Since each value may be ±10%, each value may be 20% higher than the previous one. This means that the 10% series consists of the following values with the first two colour bands shown here:
10 brown-black 33 orange-orange 12 brown-red 39 orange-white 15 brown-green 47 yellow-violet 18 brown-grey 56 green-blue 22 red-red 68 blue-grey 27 red-violet 82 grey-red
The third colour band provides the magnitude (power of 10) for the value of the resistor.
The 5% series works the same way, but since each resistor can vary by ±5%, each value is 10% higher than the previous one. This means that the 5% series consists of the following values with the first two colour bands shown here:
10 brown-black 33 orange-orange 11 brown-brown 36 orange-blue 12 brown-red 39 orange-white 13 brown-orange 43 yellow-orange 15 brown-green 47 yellow-violet 16 brown-blue 51 green-brown 18 brown-grey 56 green-blue 20 red-black 62 blue-red 22 red-red 68 blue-grey 24 red-yellow 75 violet-green 27 red-violet 82 grey-red 30 orange-black 91 white-brown
So there you have it. If you need 475 ohms, then simply use a 470 ohm resistor.