Apache isn't an operating system. It is actually completely irrelevant to Red5. An operating system would be like, Debian, CentOS, Red Hat, Windows, etc.

And no, there is no such thing as a free remote server. Nobody just gives up bandwidth and server space for free.

Your best bet is to install it on your own. If you have root access to the server, you shouldn't have any issues at all. Red5 is actually pretty easy to install.