Find the slope and the equation of the line passing through the points:

Slope of equation can be calculated using

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \Rightarrow \frac{-7-(-2)}{-5-3}=\frac{-5}{-8}$

$m=\frac{5}{8}$

Now using two point form of the equation of a line

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$ where $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=$ slope of line

$y-(-2)=\frac{5}{8}(x-3) \Rightarrow 8(y+2)=5(x-3)$

$8 y+16=5 x-15$

$5 x-8 y-16-15=0$

$5 x-8 y-31=0$

So, required equation of line is 5x - 8y - 31 = 0.