Install MongoDB:
First create a mongodb yum repository /etc/yum.repos.d/mongodb.repo, For 64-bit, use:

[mongodb]
name=MongoDB Repository
baseurl=http://downloads-distro.mongodb.org/repo/redhat/os/x86_64/
gpgcheck=0
enabled=1

Install via yum:

yum install mongodb-org

Download, compile, and install node, then install npm:

wget http://nodejs.org/dist/v0.10.28/node-v0.10.28.tar.gz
tar -xzf node-v0.10.28.tar.gz
cd node-v0.10.28
less README.md
./configure
make install
node --version
curl https://www.npmjs.org/install.sh | sh