Graph Coloring · Hard problem

A review committee has reviewers $1,2,3,4,5$. Reviewers $1,2,3$ all conflict with one another (edges $12,13,23$), reviewer $4$ conflicts only with reviewer $1$ (edge $14$), and reviewer $5$ conflicts only with reviewer $2$ (edge $25$). A schedule with $k$ time slots assigns each reviewer to one of the $k$ slots so that no two conflicting reviewers share a slot. What is the smallest $k$ for which at least $200$ different valid schedules exist?