Conditional Convergence of an Alternating Series

For which values of $p$ is the series $\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^n}{n^p + 5}$ conditionally convergent?

I. $p = \frac{1}{2}$

II. $p = 1$

III. $p = \frac{3}{2}$