Use the binomial series to find the first 5 nonzero terms of the power series centered at $x=0$ for the following function and then give the open interval of convergence for the full power series.

$$f(x) = \frac{1}{(3+x)^{5}}$$

$f(x) =$ $+$ $+$ $+$ $+$ $+ \cdots$

The open interval of convergence is: (Give your answer in interval notation.)