Hand gesture recognition (HGR) is a vital component in enhancing the human-computer interaction experience, particularly in multimedia applications, such as virtual reality, gaming, smart home automation systems, etc. Users can control and navigate through these applications seamlessly by accurately detecting and recognizing gestures. However, in a real-time scenario, the performance of the gesture recognition system is sometimes affected due to the presence of complex background, low-light illumination, occlusion problems, etc. Another issue is building a fast and robust gesture-controlled human-computer interface (HCI) in the real-time scenario. The overall objective of this paper is to develop an efficient hand gesture detection and classification model using a channel-pruned YOLOv5-small model and utilize the model to build a gesture-controlled HCI with a quick response time (in ms) and higher detection speed (in fps). First, the YOLOv5s model is chosen for the gesture detection task. Next, the model is simplified by using a channel-pruned algorithm. After that, the pruned model is further fine-tuned to ensure detection efficiency. We have compared our suggested scheme with other state-of-the-art works, and it is observed that our model has shown superior results in terms of mAP (mean average precision), precision (\%), recall (\%), and F1-score (\%), fast inference time (in ms), and detection speed (in fps). Our proposed method paves the way for deploying a pruned YOLOv5s model for a real-time gesture-command-based HCI to control some applications, such as the VLC media player, Spotify player, etc., using correctly classified gesture commands in real-time scenarios. The average detection speed of our proposed system has reached more than 60 frames per second (fps) in real-time, which meets the perfect requirement in real-time application control.