[tex]k: y = mx + b[/tex]
[tex]l: y = nx + c[/tex]
[tex]l\ \perp\ k\ \iff\ m\cdot n = -1[/tex]
We have:
[tex]k:\ f(x)=5x-8\\\\l:\ g(x)=mx+b\\\\l\ \perp\ k\iff 5m=-1\ \ \ |:5\to m=-\dfrac{1}{5}[/tex]
therefore
[tex]l:\ y=-\dfrac{1}{5}x+b[/tex]
The line passing through the point (5; 10).
Substitute the values of the coordinates of the point
[tex](5;\ 10)\to x=5;\ y=10\\\\10=-\dfrac{1}{5}\cdot5+b\\\\10=-1+b\ \ \ \ |+1\\\\b=11[/tex]
[tex]Answer:\ \boxed{y=-\dfrac{1}{5}x+11}[/tex]
