Graph Coloring · Hard problem

Two pentagons share exactly one common vertex $0$: the first is $0,1,2,3,4$ (edges $01,12,23,34,40$) and the second is $0,5,6,7,8$ (edges $05,56,67,78,80$) — $9$ vertices, $10$ edges total, and no triangle anywhere. What is the chromatic number of this combined graph?