# I wish there was a $$\displaystyle\sum_{x=0}^{n}$$ on the left instead!

Calculus Level 5

If the value of the following limit

$\lim\limits_{n \to \infty} \dbinom{n}{x} \displaystyle\left( \frac{m}{n}\right)^{x}\displaystyle\left( 1-\frac{m}{n}\right)^{n-x}$

for $$x=5$$ and $$m=5$$ is $$S$$, evaluate $$\left \lfloor{1000S}\right \rfloor$$.

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