For a description of the Hoffman-Singleton graph, and several references, see its MathWorld page. There you will find "A beautiful symmetric embedding due to E. Pegg Jr.". (This actually a drawing rather than an embedding; the graph is not planar.) The drawing obviously has a rotational symmetry of order 5. It also has the property that vertices that are adjacent on the circle are adjacent in the graph. I did a computer search for all circular drawings with these two properties. There are 666 of them; here are pictures of a few. Should you care, here is a text file containing all 666. The vertices are numbered from 0 to 49 around the circle, and for each drawing there is one line for each of the vertices 0-9 listing the seven neighbors. (The neighbors of the other vertices of course follow from the symmetry.)