I am using Windows 7 OS. I just installed jaspersoft server which installed Apache Tomcat and mysql as a bundle along with it.
I go to http://localhost:8080
The port 8005 is used as service port. You can send a shutdown command (a configurable password) to that port. It will not "speak" HTTP, so you cannot use your browser to connect.
The default port for delivering web-content is 8080.
But there may be other applications listen to that port. So your tomcat may not start, if the port is not available.
You asked "How do you know, if tomcat server is installed on your PC?". The answer to that question is: You can't
You can't determine, if it is installed, because it may be only extracted from a ZIP archive or packaged within another application (Like JBoss AS (I think)).