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.