The quality of streaming video depends on accurate estimation of network throughput, which is challenging in mobile networks due to a highly volatile environment. We used data traces obtained from measurements in 4G and 5G mobile networks, supplied them to an LSTM network and received a prediction of throughput for the next four seconds. Next, we took three dynamic adaptive streaming over HTTP (DASH) algorithms and replaced their default throughput estimation based on moving averages with the LSTM prediction. As the experiment shows, the traffic prediction improved the effectiveness of network capacity utilisation and stability of video playback between 5% and 25% compared to the default estimation. Our approach relies only on past throughput measurements, does not require any modifications to network infrastructure or protocols and is implementable in any DASH player.