I choose a random integer $n$ between $1$ and $10$ inclusive. What is the probability that for the $n$ I chose, there exist no real solutions to the equation $x(x+5) = -n$? Express your answer as a common fraction

There are 4 integers for which there is no real solution. They are: 7, 8, 9, 10

Therefore, the probability is =4 / 10 = 2 /5