Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2}+5x+5=0$

(N/A) Comparing the given equation $x^{2}+5x+5=0$ with the standard quadratic form $ax^{2}+bx+c=0$,we get:
$a=1, b=5, c=5$
The discriminant $D$ is given by the formula $D = b^{2}-4ac$.
Substituting the values:
$D = (5)^{2} - 4(1)(5)$
$D = 25 - 20$
$D = 5$
Since $D > 0$,the quadratic equation has two distinct real roots. Furthermore,since $5$ is not a perfect square,the roots are irrational.