Separate a point from a closed set in a metrizable space

Let \(X\) be a metrizable space, let \(p\in X\), and let \(C\subseteq X\) be closed with \(p\notin C\). Prove that there are disjoint open sets \(U,V\subseteq X\) such that \[ p\in U,\qquad C\subseteq V. \]