There are several ways of doing it, but really they all come down to proportions - how big is the slice of cake that each person gets. You know you want the voltage split up into 5 different voltages, so you need to work out what the difference between each of those 5 voltages is and you can then work what value each resistor is proportionally to the others.
I have attached a picture which simplifies your problem, and then works it through until you can find every resistor value based on just one.
In this case, you just have to pick a value of R2, and work out the rest from there.
If you want to use standard values, then you have to use a bit of trial and error to get as close as you can. In this case, if you pick R2 = 1.5k, you get R1 ~= 5.6k, and R6 = 3.75k. R6 can be made approximately with a 470R and a 3.3k resistor in series.
