How do I create a web browser game using UE5? (A game that isn't installed, but played in the browser)

Absolutely! Unreal Engine offers a plugin called Pixel Streaming that you can enable in your project. Once enabled, package your project and upload your build to a pixel streaming platform or even set up your own pixel streaming servers.

We used a platform called Streampixel. They charge €99 per month for unlimited streaming minutes.

Hope this helps!