  We evaluate the fifth order normalized cumulant, known as hyperskewness, of
height fluctuations dictated by the $(1+1)$-dimensional KPZ equation for the
stochastic growth of a surface on a flat geometry in the stationary state. We
follow a diagrammatic approach and invoke a renormalization scheme to calculate
the fifth cumulant given by a connected loop diagram. This, together with the
result for the second cumulant, leads to the hyperskewness value $\widetilde{S}
= 0.0835$.
