If \( f^{(n)}(5)=\frac{(-1)^{n} n!}{4^{n}(n+3)} \) for \( n=0,1,2, \ldots \), then the Taylor series for \( f \) centered at 5 is
\[
f(x)=\sum_{n=0}^{\infty} \square(x-5)^{n}
\]
\[
f(x)=\square+\square(x-5)+\square(x-5)^{2}+\square(x-5)^{3}+\ldots
\]
