How do you install MySQL 5.1.34 on CentOS 5.5?
While I would normally not recommend this
To download and install MySQL 5.1.34, run these commands at your Linux prompt AS IS...
MYSQL_VERSION=5.1
MYSQL_VERSION_RELNUM=34
MYSQL_VERSION_RELEASE=${MYSQL_VERSION}.${MYSQL_VERSION_RELNUM}
REDHAT_RELEASE=5
BINARY_VERSION=x86_64
PERL_LOCATION=ftp://ftp.de.netclusive.de/pub/parallels/Plesk/Expand/2.3.1/packages
PERL_FILE=perl-DBI-1.53-2.fc7.x86_64.rpm
PERL_URL=${PERL_LOCATION}/${PERL_FILE}
MYSQL_MIRROR_INDEX=0
MYSQL_SHARE2_LIB=MySQL-shared-compat-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
MYSQL_SHARED_LIB=MySQL-shared-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
MYSQL_DEVEL__LIB=MySQL-devel-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
MYSQL_CLIENT_LIB=MySQL-client-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
MYSQL_SERVER_LIB=MySQL-server-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
MYSQL_SHARE2_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SHARE2_LIB}&quot;
MYSQL_SHARED_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SHARED_LIB}&quot;
MYSQL_DEVEL__URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_DEVEL__LIB}&quot;
MYSQL_CLIENT_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_CLIENT_LIB}&quot;
MYSQL_SERVER_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SERVER_LIB}&quot;
cd
rm -rf MySQLInstall
mkdir  MySQLInstall
cd     MySQLInstall
wget ${PERL_URL}
wget ${MYSQL_SHARE2_URL}
wget ${MYSQL_SHARED_URL}
wget ${MYSQL_DEVEL__URL}
wget ${MYSQL_CLIENT_URL}
wget ${MYSQL_SERVER_URL}
pwd
ls -l
rpm -Uvh --force ${PERL_FILE}
rpm -Uvh --force ${MYSQL_SHARE2_LIB}
rpm -Uvh --force ${MYSQL_SHARED_LIB}
rpm -Uvh --force ${MYSQL_DEVEL__LIB}
rpm -Uvh --force ${MYSQL_CLIENT_LIB}
rpm -Uvh --force ${MYSQL_SERVER_LIB}

To go get the Latest Version of MySQL, run these AS IS...
HOWMANYBITS=64
WHATOS=5
BINARY_VERSION=000
if [ ${HOWMANYBITS} -eq 32 ] ; then BINARY_VERSION=i386   ; fi
if [ ${HOWMANYBITS} -eq 64 ] ; then BINARY_VERSION=x86_64 ; fi
MINOR_RELEASE=20
MYSQL_RELEASE=5.5.${MINOR_RELEASE}
OS_VERSION=000
if [ ${WHATOS} -eq 0 ] ; then OS_VERSION=linux2.6 ; fi
if [ ${WHATOS} -eq 5 ] ; then OS_VERSION=rhel5    ; fi
RELEASE_TAG=1
DEVEL__RPM=http://www.mysql.com/get/Downloads/MySQL-5.5/MySQL-devel-${MYSQL_RELEASE}-${RELEASE_TAG}.${OS_VERSION}.${BINARY_VERSION}.rpm/from/http://mysql.mirrors.pair.com/
SHARD2_RPM=http://www.mysql.com/get/Downloads/MySQL-5.5/MySQL-shared-compat-${MYSQL_RELEASE}-${RELEASE_TAG}.${OS_VERSION}.${BINARY_VERSION}.rpm/from/http://mysql.mirrors.pair.com/
SHARED_RPM=http://www.mysql.com/get/Downloads/MySQL-5.5/MySQL-shared-${MYSQL_RELEASE}-${RELEASE_TAG}.${OS_VERSION}.${BINARY_VERSION}.rpm/from/http://mysql.mirrors.pair.com/
CLIENT_RPM=http://www.mysql.com/get/Downloads/MySQL-5.5/MySQL-client-${MYSQL_RELEASE}-${RELEASE_TAG}.${OS_VERSION}.${BINARY_VERSION}.rpm/from/http://mysql.mirrors.pair.com/
SERVER_RPM=http://www.mysql.com/get/Downloads/MySQL-5.5/MySQL-server-${MYSQL_RELEASE}-${RELEASE_TAG}.${OS_VERSION}.${BINARY_VERSION}.rpm/from/http://mysql.mirrors.pair.com/
PERL_LOCATION=ftp://ftp.de.netclusive.de/pub/parallels/Plesk/Expand/2.3.1/packages
PERL_FILE=perl-DBI-1.53-2.fc7.x86_64.rpm
PERL_URL=${PERL_LOCATION}/${PERL_FILE}
cd
rm -rf MySQL5.5_Install
mkdir MySQL5.5_Install
cd MySQL5.5_Install
wget ${PERL_URL}
wget ${DEVEL__RPM}
wget ${SHARD2_RPM}
wget ${SHARED_RPM}
wget ${CLIENT_RPM}
wget ${SERVER_RPM}
ls -l
for RPM in `ls -lSr *.rpm | awk '{print $9}'` ; do rpm -Uvh --force ${RPM} ; done

CAVEAT
When running the download for MySQL 5.1.34, if the RPMs for the MySQL Binaries do not get retrieved, change this line
MYSQL_MIRROR_INDEX=0

to
MYSQL_MIRROR_INDEX=1

One value or the other will work.
UPDATE 2012-02-24 14:35 EDT
I just tried getting MySQL 5.1.34 (I skipped the install part) and I got this
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_VERSION=5.1
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_VERSION_RELNUM=34

[redwards@lw-lts-155 MySQLInstall]$ MYSQL_VERSION_RELEASE=${MYSQL_VERSION}.${MYSQL_VERSION_RELNUM}
[redwards@lw-lts-155 MySQLInstall]$ REDHAT_RELEASE=5
[redwards@lw-lts-155 MySQLInstall]$ BINARY_VERSION=x86_64
[redwards@lw-lts-155 MySQLInstall]$ PERL_LOCATION=ftp://ftp.de.netclusive.de/pub/parallels/Plesk/Expand/2.3.1/packages
MYSQL_SERVER_LIB=MySQL-server-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
MYSQL_SHARE2_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SHARE2_LIB}&quot;
MYSQL_SHARED_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SHARED_LIB}&quot;
MYSQL_DEVEL__URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_DEVEL__LIB}&quot;
[redwards@lw-lts-155 MySQLInstall]$ PERL_FILE=perl-DBI-1.53-2.fc7.x86_64.rpm
[redwards@lw-lts-155 MySQLInstall]$ PERL_URL=${PERL_LOCATION}/${PERL_FILE}
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_MIRROR_INDEX=0
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_SHARE2_LIB=MySQL-shared-compat-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_SHARED_LIB=MySQL-shared-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_DEVEL__LIB=MySQL-devel-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_CLIENT_LIB=MySQL-client-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_SERVER_LIB=MySQL-server-community-${MYSQL_VERSION_RELEASE}-${MYSQL_MIRROR_INDEX}.rhel${REDHAT_RELEASE}.${BINARY_VERSION}.rpm
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_SHARE2_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SHARE2_LIB}&quot;
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_SHARED_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SHARED_LIB}&quot;
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_DEVEL__URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_DEVEL__LIB}&quot;
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_CLIENT_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_CLIENT_LIB}&quot;
[redwards@lw-lts-155 MySQLInstall]$ MYSQL_SERVER_URL=&quot;http://downloads.mysql.com/archives/mysql-${MYSQL_VERSION}/${MYSQL_SERVER_LIB}&quot;
[redwards@lw-lts-155 MySQLInstall]$ cd
[redwards@lw-lts-155 ~]$ rm -rf MySQLInstall
[redwards@lw-lts-155 ~]$ mkdir  MySQLInstall
[redwards@lw-lts-155 ~]$ cd     MySQLInstall
[redwards@lw-lts-155 MySQLInstall]$ wget ${PERL_URL}
--2012-02-24 14:26:08--  ftp://ftp.de.netclusive.de/pub/parallels/Plesk/Expand/2.3.1/packages/perl-DBI-1.53-2.fc7.x86_64.rpm
           =&gt; `perl-DBI-1.53-2.fc7.x86_64.rpm'
Resolving ftp.de.netclusive.de... 89.110.128.25
Connecting to ftp.de.netclusive.de|89.110.128.25|:21... connected.
Logging in as anonymous ... Logged in!
==&gt; SYST ... done.    ==&gt; PWD ... done.
==&gt; TYPE I ... done.  ==&gt; CWD /pub/parallels/Plesk/Expand/2.3.1/packages ... done.
==&gt; SIZE perl-DBI-1.53-2.fc7.x86_64.rpm ... 625843
==&gt; PASV ... done.    ==&gt; RETR perl-DBI-1.53-2.fc7.x86_64.rpm ... done.
Length: 625843 (611K)

100%[=============================================================================================================================&gt;] 625,843      767K/s   in 0.8s

2012-02-24 14:26:10 (767 KB/s) - `perl-DBI-1.53-2.fc7.x86_64.rpm' saved [625843]

[redwards@lw-lts-155 MySQLInstall]$ wget ${MYSQL_SHARE2_URL}
--2012-02-24 14:26:10--  http://downloads.mysql.com/archives/mysql-5.1/MySQL-shared-compat-5.1.34-0.rhel5.x86_64.rpm
Resolving downloads.mysql.com... 156.151.63.14
Connecting to downloads.mysql.com|156.151.63.14|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 5058961 (4.8M) [application/octet-stream]
Saving to: `MySQL-shared-compat-5.1.34-0.rhel5.x86_64.rpm'

100%[=============================================================================================================================&gt;] 5,058,961    518K/s   in 9.7s

2012-02-24 14:26:21 (512 KB/s) - `MySQL-shared-compat-5.1.34-0.rhel5.x86_64.rpm' saved [5058961/5058961]

[redwards@lw-lts-155 MySQLInstall]$ wget ${MYSQL_SHARED_URL}
--2012-02-24 14:26:22--  http://downloads.mysql.com/archives/mysql-5.1/MySQL-shared-community-5.1.34-0.rhel5.x86_64.rpm
Resolving downloads.mysql.com... 156.151.63.14
Connecting to downloads.mysql.com|156.151.63.14|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 1827818 (1.7M) [application/octet-stream]
Saving to: `MySQL-shared-community-5.1.34-0.rhel5.x86_64.rpm'

100%[=============================================================================================================================&gt;] 1,827,818    487K/s   in 3.7s

2012-02-24 14:26:26 (487 KB/s) - `MySQL-shared-community-5.1.34-0.rhel5.x86_64.rpm' saved [1827818/1827818]

[redwards@lw-lts-155 MySQLInstall]$ wget ${MYSQL_DEVEL__URL}
--2012-02-24 14:26:26--  http://downloads.mysql.com/archives/mysql-5.1/MySQL-devel-community-5.1.34-0.rhel5.x86_64.rpm
Resolving downloads.mysql.com... 156.151.63.14
Connecting to downloads.mysql.com|156.151.63.14|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 8693623 (8.3M) [application/octet-stream]
Saving to: `MySQL-devel-community-5.1.34-0.rhel5.x86_64.rpm'

100%[=============================================================================================================================&gt;] 8,693,623    512K/s   in 17s

2012-02-24 14:26:46 (511 KB/s) - `MySQL-devel-community-5.1.34-0.rhel5.x86_64.rpm' saved [8693623/8693623]

[redwards@lw-lts-155 MySQLInstall]$ wget ${MYSQL_CLIENT_URL}
--2012-02-24 14:26:46--  http://downloads.mysql.com/archives/mysql-5.1/MySQL-client-community-5.1.34-0.rhel5.x86_64.rpm
Resolving downloads.mysql.com... 156.151.63.14
Connecting to downloads.mysql.com|156.151.63.14|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 7515446 (7.2M) [application/octet-stream]
Saving to: `MySQL-client-community-5.1.34-0.rhel5.x86_64.rpm'

100%[=============================================================================================================================&gt;] 7,515,446    501K/s   in 15s

2012-02-24 14:27:03 (497 KB/s) - `MySQL-client-community-5.1.34-0.rhel5.x86_64.rpm' saved [7515446/7515446]

[redwards@lw-lts-155 MySQLInstall]$ wget ${MYSQL_SERVER_URL}
--2012-02-24 14:27:03--  http://downloads.mysql.com/archives/mysql-5.1/MySQL-server-community-5.1.34-0.rhel5.x86_64.rpm
Resolving downloads.mysql.com... 156.151.63.14
Connecting to downloads.mysql.com|156.151.63.14|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 20053095 (19M) [application/octet-stream]
Saving to: `MySQL-server-community-5.1.34-0.rhel5.x86_64.rpm'

100%[=============================================================================================================================&gt;] 20,053,095   506K/s   in 42s

2012-02-24 14:27:46 (462 KB/s) - `MySQL-server-community-5.1.34-0.rhel5.x86_64.rpm' saved [20053095/20053095]

[redwards@lw-lts-155 MySQLInstall]$ pwd
/home/lw-staff/redwards/MySQLInstall
[redwards@lw-lts-155 MySQLInstall]$ ls -l
total 42832
-rw-r--r-- 1 redwards users  7515446 Apr  7  2009 MySQL-client-community-5.1.34-0.rhel5.x86_64.rpm
-rw-r--r-- 1 redwards users  8693623 Apr  7  2009 MySQL-devel-community-5.1.34-0.rhel5.x86_64.rpm
-rw-r--r-- 1 redwards users 20053095 Apr  7  2009 MySQL-server-community-5.1.34-0.rhel5.x86_64.rpm
-rw-r--r-- 1 redwards users  1827818 Apr  7  2009 MySQL-shared-community-5.1.34-0.rhel5.x86_64.rpm
-rw-r--r-- 1 redwards users  5058961 Apr  7  2009 MySQL-shared-compat-5.1.34-0.rhel5.x86_64.rpm
-rw-r--r-- 1 redwards users   625843 Feb 24 14:26 perl-DBI-1.53-2.fc7.x86_64.rpm

Keep in mind that the MySQL Binaries are three years old