Similar to the posts for Tomcat 6 (here) and Tomcat 7 (part 1 / part 2). This post (and Management Pack) are very similar to the previous posting with some slight platform variations.
The names of the MBeans class (and packages) representing Web Modules are different from Tomcat 7 and Tomcat 6. In Tomcat 5.5, the correct class name is org.apache.commons.modeler.BaseModelMBean. It so happens that the MP logic contains some filtering, thus the appropriate strings have been changed.
Like Tomcat 6, Tomcat 5.5.x needs to be configured to have a user account with the manager role. For this, edit the server.xml file as detailed in the Apache Tomcat documentation: http://tomcat.apache.org/tomcat-5.5-doc/manager-howto.html.
Again, I have done all of this work for you. All you need to do is import the attached MP and add the appropriate credential information.
In SCOM Console, go to Administration > Run As Configuration > Accounts and choose the task to Create Run As Account. Create a new Basic Authentication Run As Account with credentials that are appropriate for your Tomcat 5.x instance(s).
Next go to Administration > Run As Configuration > Profiles, select the Privileged Tomcat 5.x Account, and right-click and choose Properties.Associate the Account create above with the Profile.
Now all that is necessary is for the discovery to occur. Due the internals of how SCOM works, this will occur one application at a time (recall that I mentioned above that the discovery needs to run for each application). When the discovery has occurred you will three tasks for a selected application to start, stop, and restart the application.