From Zimbra :: Wiki

Article Information
This article applies to the following ZCS versions.
ZCS 4.5

Introduction

Zimbra Collaboration Suite 4.5.6 is the first version of ZCS that provides support on the Red Hat Enterprise Linux 5 (RHEL5) platform. This article describes the high level procedures in upgrading an existing ZCS installation from RHEL4 to RHEL5.
Note: We currently don't support RedHat Cluster (RHCS) on RHEL5. There is currently no date to support it.

Procedures

1. Upgrade to ZCS 4.5.6 (build 1044) RHEL4/RHEL4_64.
2. Run the following command as root,

chkconfig zimbra off

3. Make sure that the Security Enhanced Linux (SELinux) is disabled by setting the following in /etc/selinux/config:

SELINUX=disabled

4. Upgrade the Operating System to RHEL5/RHEL5_64 by selecting the "Upgrade an existing installation" option.
5. Upgrade ZCS to 4.5.6 (build 1044) RHEL5/RHEL5_64.

Ignore the following error:

Backing up ldap
/opt/zimbra/openldap/sbin/slapcat: error while loading shared libraries: libssl.so.4: cannot open shared object file: No such file or
directory