Yes, you can put your in5 exported content on your Squarespace website.
Because you're using Squarespace, the process of publishing your content requires both
For uploading your in5 content, you may be able to upload the files to Squarespace, or you can put them on GitHub if you need free place to upload them.
For other free hosting options, there are some workarounds for hosting via cloud services (many cloud services, such as Dropbox
, no longer allow their service to be used to host content). Here's an article with more information about the workarounds:
From within Squarespace, you'll need to have an iframe with the URL to wherever you have uploaded the content. You may need to confirm with Squarespace support whether to use Code Block or Embed Block to embed it.
Here is more information on embedding content using an iframe: