The quadratic $x^2 + 5x + c$ has roots in the form of $x = \frac{-5 \pm \sqrt{c}}{2}$. What is the value of $c$?
To find the value of $c$, I need to use the fact that the roots of a quadratic equation are given by the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Comparing this formula with the given roots, I can see that $a = 1$, $b = 5$, and $\sqrt{b^2 - 4ac} = \sqrt{c}$. Squaring both sides of the last equation, I get $b^2 - 4ac = c$. Substituting the values of $a$ and $b$, I get $5^2 - 4(1)c = c$. Simplifying, I get $25 - 4c = c$. Adding $4c$ to both sides, I get $25 = 5c$. Dividing both sides by $5$, I get $c = 5$. 