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Let $f(x)$ be a function such that $\lim \limits_{h \to 0} \frac{f(5+h)-f(5)}{h}=7$. Which of the following statements is true?

$\lim \limits_{x \to 5} f(x)$ does not exist.

$f(x)$ is not defined at $x=5$.

$f(5)=7$

$f(x)$ is continuous at $x=5$.