With ffmpeg, the positioning of the options matters. With your example, it is trying to apply -ss and -t to the input. Use it like this will apply the options to the output instead:
ffmpeg -i outofsight.mp4 -ss 01:15:51 -t 00:05:59 -acodec copy -vcodec copy clip.mp4
With current ffmpeg, the correct syntax would be:
ffmpeg -i outofsight.mp4 -ss 01:15:51 -t 00:05:59 -c copy clip.mp4