All of this is really to do with your host setup. Once you have the host setup sorted out, you can have multiple C5 installs each in their own subfolders with their own domains, or subdomains of a single domain. Or you could have 1 C5 install serving a number of domains.

But all that is later. What you have to do now is get your host directory structure and domains set up right. It would be the same problem for static html pages or any cms.

The first trick is never never ever never ever have your domain name mapped to the root directory of your web space.

Create a directory structure like
/webroot/my_sitename/content/
and map your domainhttp://www.mysitename.com to that directory.

This means that you can now do 2 things:
1. Have another domainhttp://www.myothersitename.com mapped to the directory
/webroot/my_other_sitename/content/

2. In the future work on a new version of your existing site in parallel,http://www.new.mysitename.com at directory
/webroot/my_sitename/content2/

To make this work, you need to understand how to map and setup domains and subdomains in your web hosts control panel. ie. Host Setup.

Note, none of the above is specific to Concrete5. Its just general good planning for any long term web project.