It appears that the group has a name of "Development Tools" and an id of "development", so you should use one of those two names with yum.

yum groupinstall 'Development Tools'

or

yum groupinstall development

To see a list of available groups, use:

yum grouplist

... among which you may see:

...
   Desktop Platform Development
   Development tools
   Dial-up Networking Support
...

You can get the id of a group using the -v flag:

yum groupinfo -v 'Development tools'

Results in (partial output):

...
Group: Development tools
 Group-Id: development
 Description: A basic development environment.
...

I added base Red Hat repository with the following commands :

cd /etc/yum.repo.d
wget http://public-yum.oracle.com/public-yum-el5.repo
cd /etc/pki/rpm-gpg/
wget https://public-yum.oracle.com/RPM-GPG-KEY-oracle-el5

Now yum install make works.

Group install just installs some group of packages (= all packages in a group). This can be useful when you want to install gnome desktop, and instead of typing yum install gnome-session nautilus gdm <and many more> you can just run something like yum groupinstall "GNOME desktop". For servers I don't see any reason to use groupinstall and don't recommend it: don't install anything you don't really need. Use yum install <package> to install something you really want.

And, to check what's being installed with groupinstall use groupinfo: yum groupinfo "Development Libraries". To get list of all available groups run yum grouplist.