2011 AIME II Problem 15

Let P(x)=x^{2}-3 x-9. A real number x is chosen at random from the interval 5 \leq x \leq 15. The probability
that \lfloor\sqrt{P(x)}\rfloor=\sqrt{P(\lfloor x\rfloor)} is equal to \frac{\sqrt{a}+\sqrt{b}+\sqrt{c}-d}{e}, where a, b, c, d,
and e are positive integers, and none of a, b, or c is divisible by the square of a prime. Find a+b+c+d+e.