So for your site, having more storage would be useful. 5 GB is not enough for your site in the current state. But if you have a 12.6 GB website, then a 10 GB hosting account is not enough either.
In either case, you’ll need to remove files or offload them to a specialized file/image/media/document storage/sharing service and link to them from your site.
Yes, that doesn’t look as professional as having it integrated in your site. But please consider that you’re using free services. If you want a professional service, you may have to pay professional fees as well.
In our experience, 5 GB is plenty for regular website content, and most people never hit this. Most people who do hit it bring large media archives with them, which is not something we want to encourage.