A line with equation

\(y=-5x+k+5\)

is a tangent to a curve with equation

\(y=7-kx-x^2.\)

(i) Find the two possible values of \(k\).

(ii) Find, for each of your values of \(k\), the equation of the tangent, the equation of the curve, and the coordinates of the point of contact of the tangent and the curve.

(iii) Find the distance between the two points of contact.