Welcome to the Community,
each vSphere version comes with its own vSphere Client version, i.e. you need to install the required client version(s). Note that you can have multiple versions installed on the same system (e.g. v5.0, v5.1, v5.5, v6.0). Also note that as of vSphere 6.5 there will be no more Windows based vSphere Client. This has been replaced with a Web Client. For ESXi the Wb Client can be accessed via https://<esxhost-or-ipaddress>/ui
André