HTML5 is generally a rather vague umbrella term used to indicate an animation (interactive or otherwise), a game, or web app running in the browser that uses a variety of web technologies, which inlcude (in this case animation):
- the use of HTML DOM elements which are moved/animated using Javascript and/or CSS animations;
- the use of SVG files with animated elements, again moved/animated using either Javascript, CSS, or both;
- the use of the CANVAS html element to draw animated objects, which relies on Javascript;
- the use of WebGL 3d to render animated 2d and/or 3d objects in the browser;
- the use of WebAssembly and WebGL to draw 2d and 3d animated elements in the browser;
- the combined use of any of the above.
Which method(s) to use depends on the type of animation, game, project, or your own preferences.
Since it is a simple animated GIF you made in Photoshop, I assume it is a simple 2d animation. And based on your post, I also assume you have little or no experience with web development or coding.
In that case options would be:
Other options would include libraries such as GSAP (which requires programming knowledge), or even HTML5 game creators like Construct 3 (which also includes an animation timeline). And there are many other developer tools and libraries available online and offline for free and money that could be used as well.
It is not possible to directly convert your existing Photoshop animation to any of these tools, though. Photoshop has no option to export to one of the earlier mentioned HTML 5 options. The best that you can achieve is to import the layered PSD (if supported by the tool) or export all your layers as separate assets, and re-do your animation in the tool of your choice.
(There might be Photoshop plugins to help you with this process as well, perhaps even direct converters. I have not Googled that, because in my experience similar plugins cost an arm and a leg, and are too limited anyway.)