Summary: A convex geometry is a closure system satisfying the antiexchange property. We document all convex geometries on 4- and 5-element base sets with respect to their representation by circles on the plane. All 34 nonisomorphic geometries on a 4-element set can be represented by circles, and of 672 known geometries on a 5-element set, we give representations for 623. Of the 49 remaining geometries on a 5-element set, one was already shown not to be representable due to the weak carousel property, as articulated by K. Adaricheva and M. Bolat [Discrete Math. 342, No. 3, 726–746 (2019; Zbl 1409.52001)]. We show that seven more of these convex geometries cannot be represented by circles on the plane, due to what we term the triangular implications property.