Installing on existing site

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Hello -
I have an existing site that has grown (sprawled) over time, and concrete5 seems a great system to bring in into some order. When I installed c5, I put it in its own folder, and find the home page created for me is inside the c5 directory, which is not what I want.

I've seen many posts about modifying the c5/config/site.php file's Base_URL and DIR_REL, but can't get it to realize that the site is above the c5 directory.

I then noticed that the c5/concrete folder contains the same directories as the c5 directory, so I tried copying all the files from concrete to the root directory, with all my other files.

I'm not a stupid person, and I've been working on my site for seven years, so I'm not a beginner. But setting up concrete5 in my environment has me completely baffled, and after two days of searching this site, and testing a lot of theories, I give up and have to ask.

Topics on moving sites seem like they might be relevant, but I don't want to move anything, nor do I want to move my thousands of files into a sub directory, which seems like SEO suicide.

How can I achieve what I want to do: Have the backend in the c5 directory on my site, and have my site pages and directories in root?