The Chain Rule & Implicit Differentiation · Superchallenge problem

In $\mathbb R^5$, let $r = |\mathbf x| = \sqrt{x_1^2 + \cdots + x_5^2}$. Find the nonzero real number $p$ for which $u = r^p$ is harmonic ($\sum_{i=1}^5 u_{x_ix_i} = 0$) on $\mathbb R^5\setminus\{\mathbf 0\}$.