Redmine is not available on CentOS-5 machines.

Newer versions of Redmine work with a passenger version that is no longer possible to compile on our CentOS 5 machines.

You can create a 'custom app (listening on port)' type of application and then follow the official instructions to install the latest redmine version using ruby2.2 and a server like unicorn.

I've managed to get one up and running by doing the following:

cd ~/webapps/<app_name>
mkdir gems tmp
export TMP=$PWD/tmp
export GEM_HOME=$PWD/gems
export RUBYLIB=$GEM_HOME/lib
export PATH=$GEM_HOME/bin:$PATH
gem2.2 install bundler unicorn
curl --silent http://www.redmine.org/releases/redmine-3.2.1.tar.gz | tar xz
cd redmine-3.2.1
# create a database and user and follow [this](http://www.redmine.org/projects/redmine/wiki/redmineinstall#Step-2-Create-an-empty-database-and-accompanying-user) link to create the schema
cp config/database.yml.example config/database.yml
vi config/database.yml # edit to your needs
bundler install --without development test rmagick
vi config/secrets.yml # create as per http://guides.rubyonrails.org/upgrading_ruby_on_rails.html#config-secrets-yml
bundle exec rake secret # copy the long string
export SECRET_KEY_BASE=<long_string>
RAILS_ENV=production bundle exec rake db:migrate
RAILS_ENV=production bundle exec rake redmine:load_default_data
unicorn -D -E production -p <custom_app_port>