Given points are (m, -5) and (1, 5). So, x1 = m, y1 = -5, x2 = 1, y2 = 5.

The slope $s$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$$s = \frac{y_2 - y_1}{x_2 - x_1}$$

Given points are $(m, -5)$ and $(1, 5)$. So, $x_1 = m$, $y_1 = -5$, $x_2 = 1$, $y_2 = 5$.
The given slope is $s = \frac{1}{2}$.

$$\frac{1}{2} = \frac{5 - (-5)}{1 - m}$$

$$\frac{1}{2} = \frac{5 + 5}{1 - m}$$ $$\frac{1}{2} = \frac{10}{1 - m}$$

$$1 \times (1 - m) = 2 \times 10$$ $$1 - m = 20$$

$$-m = 20 - 1$$ $$-m = 19$$ $$m = -19$$

The value of $m$ is $\boxed{-19}$.

$$\frac{2}{5} \times \frac{18}{4} = \frac{2 \times 18}{5 \times 4}$$ $$= \frac{36}{20}$$

The greatest common divisor of 36 and 20 is 4.

$$\frac{36 \div 4}{20 \div 4} = \frac{9}{5}$$

The simplified expression is $\boxed{\frac{9}{5}}$.