Find slope intercept equation 

Using the slope relationship between two perpendicular lines  $m_1m_2=-1$, any line which is perpendicular to the line $y=-2x+4$ (given) will be of the form
$$y=\frac12x+c$$ because the slope for this line is obtained using the above relationship as $m_2=-\frac{1}{-2}=\frac12$

Now, if this line  $y=\frac12x+c$  passes through the point  $(1,-5)$  then it must satisfy the equation so we get
$$-2=\frac12+c$$
$$\implies c=-\frac52$$
So, the equation of the line is $$y=\frac12x-\frac52$$

But we need to convert this equation into slope-intercept form which looks like $$\color{blue}{\frac xa+\frac yb=1}$$
$$\frac{x}{-2}+\frac y1=-\frac52$$
Multiplying both sides by $-\frac25$ we get

$$\displaystyle\boxed{\color{red}{\frac x5+\frac{y}{-\frac52}=1}}$$