This is a re­peat of a talk given ear­lier in year, with a slight im­prove­ment in proof tech­nique and (hope­fully) a large im­prove­ment in clar­ity. The Theta-five graph was shown to be a 9.96-span­ner by Bose et al., using a proof by in­duc­tion on the size of an isosce­les tri­an­gle de­fined by two points $a$ and $b$. We im­prove this bound to 5.70 using a proof by in­duc­tion on the Eu­clid­ean dis­tance be­tween $a$ and $b$. This gives us a finer grained analy­sis while main­tain­ing a com­pa­ra­ble com­plex­ity, bring­ing us closer to the lower bound of 3.798.