$f^{(5)}(x)=-\dfrac{120}{x^6}$

$f^{(5)}(x)=\dfrac{120}{x^6}$

$f^{(5)}(x)=-\dfrac{120}{x^5}$

$f^{(5)}(x)=-120\cdot x^6$

$f^{(n)}(x)=(-1)^n\cdot\dfrac{n!}{x^{(n+1)}}$

$f^{(n)}(x)=(-1)^n\cdot\dfrac{1}{x^{(n+1)}}$

$f^{(n)}(x)=\dfrac{n}{x^{(n+1)}}$

$f^{(n)}(x)=(-1)^n\cdot\dfrac{n!}{x}$