Generally speaking, there is no such thing as an “HD GIF.” Technically speaking, you may be able to make one, but nobody will be able to play it because it will be huge in file size and require massive CPU power to decode. The GIF format is literally 30 years old, and it was designed for short, small, flat color animations, not for video, and especially not for HD video.
Ideally, you would share your 5 seconds of video as video. All computing devices and TV’s — literally all of them — have MPEG-4 H.264 video decoders in them.
If you have to convert video to GIF, use a video tool to do the conversion, not a photo tool like Photoshop, and be prepared to scale the resolution of the video down to something like 25% of its current size. You will also lose almost all of the colors and clarity. The fact that the GIF format is so ancient and so technically compromised means that creating a good GIF is more of an art than a science. It is very hard to get a decent result. So if you are looking for high-quality, then that is another reason to publish your video as video.