First, let's make some observations about this question.
All points 5 units away from point (2, 7) would make a circle with center (2, 7) and radius 5.
The formula for that circle would look something like (x−2)2+(y−7)2=25
Now, combining that with the second equation, and we get a system.
Subsituting out y with the x values in the line equation, we get
(x−2)2+(5x−35)2=25
Simplifying, and we get
13x2−177x+602=0
Using the quadratic equation, we find two values of x. We get
x=7x=8613
Plugging these x values into the second equation where we isolated y, we get thatr y=7;y=6613
So our final two answers are (7, 7) and (86/13, 66/13)
Thanks! :)