Im having a bit of trouble proving a function is continuous for all reals except for one point. I can do the proof for one point but I'm having trouble extending the proof to all reals except one point.

If $\varphi(x)$ is a function from $\mathbb{R}$ to $\mathbb{R}$ such that $\varphi(x)=0$ for $x\neq5$ and $\varphi(5)=3$, prove that $\varphi$ is continuous at every $k\neq5$ using the epsilon delta definition.