Gašper Fijavž: 5th color is only needed once

 
We show that -every- 3-connected planar graph G admits a proper 5-coloring c of vertices so that 
(i) no automorphism (except the identity map) preserves both G and c 
(ii) there exists a single vertex which is colored with color 5. 
We have used the word -every- in a liberal manner: there are two exceptional graphs which fail the above property.