well, we know the slope-intercept is y=5x-3 , now [tex]\bf y=\stackrel{slope}{5}x\stackrel{y-intercept}{-3}[/tex].
reason why is called the slope-intercept form, so, the slope is 5, and we know the line runs through -2,-13, thus
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
% (a,b)
&&(~ -2 &,& -13~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 5
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-13)=5[x-(-2)]
\\\\\\
y+13=5(x+2)[/tex]