S5 1803+784 is a low synchrotron peaked (LSP) BL Lac object. Recent multiwavelength studies show no clear correlation between the synchrotron emission and the \gamma-ray emission in this blazar. Unlike most LSP blazars, the spectrum of S5 1803+784 is poorly fitted with a single zone synchrotron self-Compton (SSC) leptonic jet model. We utilize a simple single-zone leptonic jet emission model with external Compton (EC) originating from the dusty torus (DT) to explain the emission and produce the best-fit parameters. The spectral analysis of the blazar in the flaring state reported in Astronomy Telegram (ATel #13633) is studied using data from Fermi-LAT and NED archival data. We verified that the NED archival data are suitable for the spectral analysis of this blazar both during the flare and in the quiescent state by plotting the available synchrotron simultaneous data of the flare period with the NED archival data. The spectral energy distribution (SED) model of the flare and the quiescent state's best-fit parameters are produced using the Jetset code. The results constrain the upper limit of the \gamma-ray emission region length scale, the jet energetics, and the likely acceleration mechanism of the blazar during the flare.