FFmpeg is a free and open-source video editing tool capable of trimming, cropping, concatenating, muxing, and transcoding almost any type of media file you throw at it.
To remove the first seconds of a video, use the following command:
$ ffmpeg -ss 00:05 -i input.mp4 -c:v libx264 -c:a aac output.mp4
Unlike the previous example, where the video is completely re-encoded, it is also possible to cut the video without re-encoding by cutting at the nearest I-frame. Whether this works depends on how the video is encoded and where these I-frames are. That's why it doesn't cut exactly where you want it to. It can also cause some video players to have trouble playing the video. So I recommend this only if you can test the video on the players you want to support.
Here's how to cut the first 5 seconds of a video without re-encoding it:
$ ffmpeg -ss 00:05 -i input.mp4 -c:v copy -c:a copy output.mp4