To find the slope of line \( n \) that goes through points \( A(5, 4) \) and \( B(15, 12) \), we can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = A(5, 4) \) and \( (x_2, y_2) = B(15, 12) \).
Substituting these values into the formula:
\[ m = \frac{12 - 4}{15 - 5} \]
Calculating the differences in the numerator and the denominator, we get:
\[ m = \frac{8}{10} \]
To simplify \( \frac{8}{10} \):
\[ m = \frac{4}{5} \]
Thus, the slope of line \( n \) is
\[ \frac{4}{5} \]
So the answer is \( \frac{4}{5} \).