I spent two days troubleshooting this problem.

I tried the following:
- custom php.ini
- editing the master php.ini
- .htaccess
- editing httpd.conf
- editing concrete5 php files
- pouring over error logs
- and a bunch of other suggestions I'm trying to forget

all at the suggestion of various people in the forums and other google searches.

Then I noticed something. The forms to install kept complaining about being insecure even though the site I was installing had a valid SSL cert.

I set up a duplicate site on port 80 and guess what? The "supports concrete5 request URLs" error went away and I could install.