These are the Terminal commands I recently used (January 2014) to install Git 1.8.5.2 from source on CentOS 5.10. I ran this in a VirtualBox VM after a fresh install from the ISO.
You mileage will vary as the yum packages are updated over time. The yum install line below should include all the dependencies, at least it did for me. Depending upon how often you use yum update you may need to run yum --enablerepo=base clean metadata as su before you run the following commands.
cd ~/Downloads
su
yum -y install gcc make autoconf zlib-devel openssl-devel cpio expat-devel gettext-devel