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In this article, we consider the connection problem of the KZ(Knizhnik-Zamolodchikov) equation on the moduli space $\cM_{0,5}$, and showthat the connection matrices are expressed in terms of the Drinfel'dassociator. As the compatibility condition on the connection problem, we havethe pentagon relation for the Drinfeld associators. As an application of theconnection problem, we derive the five term relation for dilogarithms.

Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$