1-form on variety

Question

Let $k$ be an algebraically closed field and consider the affine curve $Z(-y^5+x^4-1) \subset \mathbb{A}^2(k)$. Define on it the rational 1-form $w=\frac{dx}{5y^4}=\frac{dy}{4x^3}$. Is there a (relatively straightforward) way to see that $w$ has no poles on the curve $\textit{without}$ calculating its order at all points?