For a wastewater sample, the three-day biochemical oxygen demand at incubation temperature of $20^{\circ}C$ (BOD$_{\text{3day}, 20^{\circ}C}$) is estimated as $200 mg/L$. Taking the value of the first order BOD reaction rate constant as $0.22 \: \text{day}^{-1}$, the five-day BOD (expressed in mg/L) of the wastewater at incubation temperature of $20^{\circ}C$ (BOD$_{\text{5day}, 20^{\circ}C}$) would be ________