Solve the equation using the quadratic formula. \[ x^{2}+9 x+5=0 \]

Step 1 ：Given the quadratic equation \(x^{2}+9 x+5=0\), we are to find the solutions for \(x\).

Step 2 ：We use the quadratic formula which is given by \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\), where \(a\), \(b\), and \(c\) are coefficients of the quadratic equation \(ax^{2} + bx + c = 0\).

Step 3 ：In this case, \(a = 1\), \(b = 9\), and \(c = 5\). We substitute these values into the quadratic formula to find the solutions for \(x\).

Step 4 ：Upon substitution, we find that the solutions to the equation are \(x = -8.405124837953327\) and \(x = -0.594875162046673\).

Step 5 ：Final Answer: The solutions to the equation \(x^{2}+9 x+5=0\) are \(\boxed{-8.405124837953327}\) and \(\boxed{-0.594875162046673}\).