What is the sum of the values of $x$ that satisfy the equation $x^2-5x+5=9$?
Subtracting 9 from both sides of the equation, we have $x^2 - 5x - 4 = 0$.  The sum of the roots of this quadratic is negative its linear coefficient, which is $\boxed{5}$.

(The above is true because if a quadratic has roots $r$ and $s$, we have $(x-r)(x-s) = x^2 - (r+s)+rs = 0$.)