After ATEL #5739 and #5784 about NIR and gamma-ray flaring activity of the quasar S5 1044+71 (2FGL J1048.3+714) we have observed it with the RATAN-600 radio telescope at frequency 4.8-21.7 GHz almost simultaneously on 22-23 January 2014. The flat spectrum (alpha= +0.00 +/-0.02)) at frequencies higher 8.2 GHz can be fitted for measured flux densities: 2.50 +/-0.14, 2.72 +/-0.19, 2.77 +/-0.24 and 2.78 +/-0.28 Jy at 4.8, 8.2, 11.2 and 21.7 GHz respectively. Such high fluxes indicate the high state of the S5 1044+71 in comparison with earlier data collected in the CATS database (cats.sao.ru).