The following procedure will walk you through the steps required to perform an in-place upgrade of vCenter and its components using the vCenter installer:

1. At first, download the latest version of vCenter 6.5 Windows ISO and map it to the machine running the current version of vCenter 5.5/6.0.
2. Browse the contents of the ISO and run the autorun.exe file as a local system administrator or with a user that has local system administrator rights, to bring up the vCenter installer.
3. On the vCenter installer screen, click on the Install button to start the installation wizard. 
4. On the Welcome to VMware vCenter Server 6.5 Installer screen, click on the Next button to continue.
5. Accept the EULA and click on the Next button to continue.
6. On the vCenter Single Sign-On and vCenter Credentials screen, supply the SSO administrator password and click on the Next button to let the installer run the pre upgrade checks.
7. On the Configure Ports screen—you are not allowed to make any changes. Click on the Next button to continue.
8. On the Upgrade Options screen, you can choose to migrate all or some of the historical data and the configuration or just the configuration. Choose an intended option and click on the Next button to continue:

9. On the Destination Directory screen, you can choose to change the Program Files and ProgramData locations for this installation. You can also choose to modify the location of the export folder, which is used by the installer to export current configuration. Make intended changes and click on Next to continue.
10. On the next screen, you can choose either join or not join VMware's Customer Experience Improvement Program. Make an intended selection and click on Next to continue.
11. On the Ready to Upgrade screen, confirm that you have backed-up your vCenter Server by selecting the checkbox I verify that I have backed up this vCenter Server machine and click on the Upgrade button.
12. The installer will now perform the upgrade, and if successful, it will display a Setup Completed wizard screen, where you click on Finish to close the wizard:
13. Once done, you should be able to log in to the Web Client to view and manage the upgraded vCenter Server. If everything looks good, you can delete the export folder to free up some disk space.