You have the installer. You double-click it. And... nothing. Or worse, you get an error stating compatibility issues.
While getting the vSphere Client 5.5 on Windows 11 is possible, it is a patchwork solution. VMware ended support for vSphere 5.5 on September 19, 2018. Using it on Windows 11 invites instability and security risks. vsphere client 5.5 download for windows 11
The installer still blocks Windows 11 via version detection. To override: You have the installer
Although the client is a desktop app, its login dialog uses IE rendering. Run the installer again
When you launch the client and try to connect to ESXi 5.5, you may get: "Client cannot send HTTP request". Fix this:
Yes, the same client works for vCenter Server 5.5. However, the vCenter 5.5 Web Client (Flash-based) is impossible on Windows 11, so the fat client is your only choice.