To find the slope of the line that passes through the points \( (8, 5) \) and \( (10, 6) \), we use the formula for the slope (\( m \)):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign the points as follows:
- \( (x_1, y_1) = (8, 5) \)
- \( (x_2, y_2) = (10, 6) \)
Now, substituting the values into the slope formula:
\[ m = \frac{6 - 5}{10 - 8} = \frac{1}{2} \]
Thus, the slope of the line is
\[ \boxed{\frac{1}{2}} \]