To find the slope of the line that passes through the points \((x_1, y_1) = (10, 8)\) and \((x_2, y_2) = (5, 16)\), we can use the formula for the slope \(m\) between two points:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the coordinates of the points:
\[ m = \frac{16 - 8}{5 - 10} \]
Calculating the differences in the numerator and the denominator:
\[ m = \frac{8}{5 - 10} = \frac{8}{-5} \]
This simplifies to:
\[ m = -\frac{8}{5} \]
Thus, the slope of the line that passes through the points \((10, 8)\) and \((5, 16)\) is
\(\boxed{-\frac{8}{5}}\).