You can access your vCenter Server using vSphere web client. vSphere web client can be accessed using the below URL
https://vSphere_Web_Client_host_name_or_IP:9443/vsphere-client
Second Method is to install vSphere Windows client 5.5 and access the vCenter server and ESXi host directly. You can only use vSphere windows client to connect to your ESXi host. ESXi host cannot be accessed directly using vSphere web client. You can also use Putty to SSH into ESXi host.
In vSphere 5.5, all new vSphere features are available only through the vSphere web client. The traditional vSphere client will continue to operate, supporting the same features set as vSphere 5.0 bu tnot exposing any new features in vSphere 5.5.The vSphere client is still used for the vSphere Update Manager and Host client along with few solutions like Site Recovery Manager.
That’s it. We are done with the update serier of vSphere 5.5. I hope this is informative for you. Thanks for Reading !!!!