vSphere Client 5.5 is not officially supported on Windows 11 , as it reached its End of General Support (EoGS) on September 19, 2018
Additional Resources
Since VMware removed direct links for version 5.5 from their main download portal, use this method: vsphere client 5.5 download for windows 11
https://<your-esxi-ip>Filename to look for: VMware-viclient-all-5.5.0-xxxxxx.exe vSphere Client 5