Calculate the height of a gable (rake) wall based on roof slope and half of the wall's horizontal length the "rake run".
convert plate length amount of 12' - 6" into inches
12 * 12 + 6 = 150 inches
roof slope; divide the rise by the run
5 ÷ 12 = 0.4166667
multiply the length of the plate by this amount
150 * 0.4166667 = 62.5
The 62.5 inches is the increase in height for the rake wall from its lowest to the highest point.
If your wall has a starting height of 96" (8 feet) the rake wall will have a total height of 96 + 62.5 = 158.5 inches = 13' - 2 1/2"