Distance 5 curves in the curve graph of closed surfaces

Let [Formula: see text] denote a closed, orientable surface of genus [Formula: see text] and [Formula: see text] be the associated curve graph. Let [Formula: see text] be the path metric on [Formula: see text] and [Formula: see text] and [Formula: see text] be a pair of curves on [Formula: see text] with [Formula: see text]. In this paper, we fix the vertex [Formula: see text] and apply the Dehn twist about [Formula: see text], [Formula: see text] to it in an attempt to create pairs of curves at a distance [Formula: see text] apart. We give a necessary and sufficient topological condition for [Formula: see text] to be at least [Formula: see text]. We also give an example of a pair of curves on [Formula: see text] which represent vertices at a distance [Formula: see text] in [Formula: see text] with intersection number [Formula: see text].