I'd recommend using yum localinstall rather than using the rpm command directly; that way you'll have the gcc package in your yum database so that it can keep track of updates. The command would just be:

yum localinstall /mnt/cdrom/CentOS/gcc-(whatever).rpm

Tru Huynh of centos.org has built the redhat developer toolset 1.1, for centos and it contains gcc 4.7.2

So you could simply use his repo and install just gcc, instantly.

cd /etc/yum.repos.d
wget http://people.centos.org/tru/devtools-1.1/devtools-1.1.repo 
yum --enablerepo=testing-1.1-devtools-6 install devtoolset-1.1-gcc devtoolset-1.1-gcc-c++

This will install it most likely into /opt/centos/devtoolset-1.1/root/usr/bin/

Then you can tell your compile process to use the gcc 4.7 instead of 4.4 with the CC variable

export CC=/opt/centos/devtoolset-1.1/root/usr/bin/gcc  
export CPP=/opt/centos/devtoolset-1.1/root/usr/bin/cpp
export CXX=/opt/centos/devtoolset-1.1/root/usr/bin/c++

Yum will install rpm from it's repository.

So I don't understand why you want to avoid yum, it will solve dependencies and install them as well.

However, here is official RPM repository mirror (one of many): http://centos.arminco.com/5/os/i386/CentOS/

Here is list of all mirrors : http://www.centos.org/modules/tinycontent/index.php?id=30

You will need at least 3 RPMs:

• gcc-4.4.6-3.el6.i686.rpm
• gcc-c++-4.4.6-3.el6.i686.rpm
• libgcc-4.4.6-3.el6.i686.rpm

For compilation of C/C++ you will also need libstdc++, glibc, etc

When you run

yum install gcc

Everything is done

As you did not specified architecture I assume i386, but URL is very similar for x86_64:

http://centos.arminco.com/6/os/x86_64/Packages/

Now devtools-8 is available and it's possible to use it by following commands:

yum install centos-release-scl
yum install devtoolset-8-gcc devtoolset-8-gcc-c++
scl enable devtoolset-8 -- bash

It's explained in a little more detail in this answer on StackOverflow: How to install GCC/G++ 8 on CentOS. And of course, if you need GFortran, you can install it in the same way - the package is devtoolset-8-gcc-gfortran.

The easiest method by far is to make use of a binary build that's provided through a YUM repository. One such option would be to use the hop5.in repository. Specifically this page: gcc - Various compilers (C, C++, Objective-C, Java, ...). They're providing 4.8.2 which should work with CentOS 6.3 or 6.4. You might want to do an update prior:

$ sudo yum update

The other option would be to make use of the Developer Toolset, specifically the bundled version provided by Scientific Linux.

• http://linux.web.cern.ch/linux/devtoolset/

Following the installation instructions you'll basically do the following 2 steps:

$ sudo wget -O /etc/yum.repos.d/slc6-devtoolset.repo \
    http://linuxsoft.cern.ch/cern/devtoolset/slc6-devtoolset.repo
$ wget -O /etc/yum.repos.d/slc5-devtoolset.repo \
    http://linuxsoft.cern.ch/cern/devtoolset/slc5-devtoolset.repo

$ sudo yum install devtoolset-2

Update #1

The hop5.in YUM repository appears to have been removed, so the only recourse is to make use of the devtoolset method highlighted above.

Additional examples for installing via devtoolset are highlighted in this GitHub Gist: Installing gcc 4.8 and Linuxbrew on CentOS 6.