Otdfbt

When I run yum update I receive the following error:

Repository 'base' is missing name in configuration, using id
Loading mirror speeds from cached hostfile
Error: Cannot find a valid baseurl for repo: base

I am not behind a proxy. Does anybody know how to fix?

You should see if /etc/yum.repos.d/CenOS-Base.repo file exists

If it does then I would reference the following to see if there is anything inside of the base repo file that may cause a error. Otherwise if the file does not exist, I would create the file with these settings to see if it will work for you.

# CentOS-Base.repo
#
# This file uses a new mirrorlist system developed by Lance Davis for CentOS.
# The mirror system uses the connecting IP address of the client and the
# update status of each mirror to pick mirrors that are updated to and
# geographically close to the client. You should use this for CentOS updates
# unless you are manually picking other mirrors.
#
# If the mirrorlist= does not work for you, as a fall back you can try the
# remarked out baseurl= line instead.
#
#

[base]
name=CentOS-$releasever - Base
mirrorlist=http://mirrorlist.centos.org/?release=5&arch=$basearch&repo=os
baseurl=http://mirror.centos.org/centos/$releasever/os/$basearch/
gpgcheck=1
gpgkey=http://mirror.centos.org/centos/RPM-GPG-KEY-CentOS-5

#released updates
[updates]
name=CentOS-$releasever - Updates
mirrorlist=http://mirrorlist.centos.org/?release=5&arch=$basearch&repo=updates
baseurl=http://mirror.centos.org/centos/$releasever/updates/$basearch/
gpgcheck=1
gpgkey=http://mirror.centos.org/centos/RPM-GPG-KEY-CentOS-5
#additional packages that may be useful

[extras]
name=CentOS-$releasever - Extras
mirrorlist=http://mirrorlist.centos.org/?release=5&arch=$basearch&repo=extras
baseurl=http://mirror.centos.org/centos/$releasever/extras/$basearch/
gpgcheck=1
gpgkey=http://mirror.centos.org/centos/RPM-GPG-KEY-CentOS-5

[centosplus]
name=CentOS-$releasever - Plus
mirrorlist=http://mirrorlist.centos.org/?release=$releasever&arch=$basearch&rep$
baseurl=http://mirror.centos.org/centos/$releasever/centosplus/$basearch/
gpgcheck=1
enabled=0
gpgkey=http://mirror.centos.org/centos/RPM-GPG-KEY-CentOS-5

[dag]
name=Dag RPM Repository for Centos
baseurl=http://apt.sw.be/redhat/el$releasever/en/$basearch/dag

[addons]
name=CentOS-$releasever - Addons
mirrorlist=http://mirrorlist.centos.org/?release=5&arch=$basearch&repo=addons
baseurl=http://mirror.centos.org/centos/$releasever/addons/$basearch/
gpgcheck=1
gpgkey=http://mirror.centos.org/centos/RPM-GPG-KEY-CentOS-5
enabled=1

I would also double check your GPG key
http://www.cyberciti.biz/faq/redhat-centos-linux-verify-rhn-rhn-repo-package-gpg-keys/

Centos 5 is in End of Life from some months.
As you can read in http://mirror.centos.org/centos/5/readme :

This directory (and version of CentOS) is depreciated.

CentOS-5 is now past EOL

You can get the last released version of centos 5.11 here:

http://vault.centos.org/5.11/

Please NOTE: this is not being maintained for security since moving to Vault.
It will have security issues, you should upgrade to a new version instead.