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We show that the slopes of the $U_5$ operator acting on 5-adic overconvergent modular forms of weight $k$ with primitive Dirichlet character $\chi$ of conductor 25 are given by either $$\left\{\frac{1}{4}·⌊\frac{8i}{5}⌋:i\in \mathbb{N}\right\}\text{or}\left\{\frac{1}{4}·⌊\frac{8i+4}{5}⌋:i\in \mathbb{N}\right\},$$ depending on $k$ and $\chi$. We also prove that the space of classical cusp forms of weight $k$ and character $\chi$ has a basis of eigenforms for the Hecke operators $T_p$ and $U_5$ which is defined over ${\mathbf{Q}}_5(\sqrt[4]{5},\sqrt{3})$.