jmc

First we find the solution set that results in the equation having no real solutions. We begin by rearranging the equation $x(x+5)=-n$ to $x^2+5x+n=0$. If the discriminant $b^2-4ac<0$, then there are no real solutions. Thus, we want to solve for $n$ in the inequality $25-4n<0$. Adding $4n$ and dividing by 4, we find $n>6.25$. The probability that I chose one of the numbers 7, 8, 9, or 10 is $\boxed{\frac{2}{5}}$.