Coordinate question

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

$13x^{2}-177x+602=0$

Using the quadratic equation, we find two values of x. We get

$x=7\\ x=\frac{86}{13}$

Plugging these x values into the second equation where we isolated y, we get that $y=7,y=\frac{66}{13}$

So our final two answers are (7, 7) and (86/13, 66/13)

Thanks! :)