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A graph \( G \) is a homomorphic preimage of another graph \( H \), or equivalently \( G \) is \( H \)-colorable, if there exists a graph homomorphism \( f: G \to H \). A classic problem is to characterize the family of homomorphic preimages of a given graph \( H \). A geometric graph \(\overline{G}\) is a simple graph \( G \) together with a straight line drawing of \( G \) in the plane with the vertices in general position. A geometric homomorphism (resp. isomorphism) \(\overline{G} \to \overline{H}\) is a graph homomorphism (resp. isomorphism) that preserves edge crossings (resp. and non-crossings). The homomorphism poset \(\mathcal{G}\) of a graph \( G \) is the set of isomorphism classes of geometric realizations of \( G \) partially ordered by the existence of injective geometric homomorphisms. A geometric graph \(\overline{G}\) is \(\mathcal{H}\)-colorable if \(\overline{G} \to \overline{H}\) for some \(\overline{H} \in \mathcal{H}\). In this paper, we provide necessary and sufficient conditions for \(\overline{G}\) to be \(C_n\)-colorable for \(3 \leq n \leq 5\).