5. A circle \(C\) has centre \(( 3,4 )\) and radius \(3 \sqrt { } 2\). A straight line \(l\) has equation \(y = x + 3\).
- Write down an equation of the circle \(C\).
- Calculate the exact coordinates of the two points where the line \(l\) intersects \(C\), giving your answers in surds.
- Find the distance between these two points.