$x^{2}-11 x+19=-5$

Step 1 ：The given equation is \(x^{2}-11 x+19=-5\).

Step 2 ：First, we move all terms to one side of the equation to set it equal to zero. This gives us \(x^{2}-11 x+24=0\).

Step 3 ：We can solve this quadratic equation using the quadratic formula, which is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where a, b, and c are the coefficients of the quadratic equation in the form \(ax^2 + bx + c = 0\).

Step 4 ：In our equation, a = 1, b = -11, and c = 24.

Step 5 ：Substituting these values into the quadratic formula gives us two solutions: \(x1 = 8.0\) and \(x2 = 3.0\).

Step 6 ：Final Answer: The solutions to the equation are \(\boxed{8.0}\) and \(\boxed{3.0}\).