Redmine

You can follow the generic upgrade path. See RedmineUpgrade.

Note though that the environmental requirements are vastly different for a current Redmine version compared to what you have there. Thus, you will likely want to install a new Redmine on a new server first. Once everything works, you can move over your existing data, i.e. the files directory and the contents of your old database which then needs to be migrated. Before starting, make sure you have a full (and working) backup of all data and your database.