Graph Coloring · Hard problem

A pentagonal prism has two pentagons, $0,1,2,3,4$ and $5,6,7,8,9$, plus a "rung" edge joining each $i$ to $i+5$ ($15$ edges total, every vertex degree $3$ — much like the Petersen graph's own degree). Unlike the Petersen graph, which needs $4$ colors to edge-color (it is a "snark"), what is the pentagonal prism's chromatic index?