$An = x^{n-1} + x^n + x^{n+1} + x^{n+2} + x^{n+3}$
e.g. $A2 = x + x^2 + x^3 + x^4 + x^5$
Notice you can only take x common out of all these terms i.e. the smallest term $x^{n - 1}$

If $\frac{An}{{x(1+x(1+x(1+x(1+x))))}} = x^5$, it means the part: (1+x(1+x(1+x(1+x)))) will get canceled from the num and den. Ignore it.
From An, you will be able to take out $x^6$ common so that $\frac{x^6}{x}$ gives you $x^5$
So smallest term must be $x^6$ i.e. $x^{n-1}$. Therefore, n = 7.

Answer: B