Hi,
Make sure you have a vCenter and VMware Update Manager database backup before start and backup of vCenter server itself, if it’s VM make a clone just before you start.
Microsoft SQL Server 2008 Enterprise (R2 SP2) - 64-bit 5.5 U2 compatible
Microsoft SQL Server 2005 Standard Edition (SP4) -64-bit 5.5 U2 compatible
Step by step upgrade the vCenter 5.1 Upgrade
Single Sign On Installation
vSphere Web Client and Inventory Service Installation
vCenter Upgrade, vSphere Client Upgrade and ESXi Host Agent Upgrade
vSphere Update Manager Install and ESXi Host Upgrade