The vSphere 5 client is a software application that allows users to manage and monitor virtual machines and ESXi hosts in a vSphere environment. If you're looking to download the vSphere 5 client, here's what you need to know:
Since vSphere 5 is obsolete, consider migrating to: vsphere 5 client download
Since direct links change, use the archive. The vSphere 5 client is a software application
If you're unable to download or use the vSphere 5 client, consider using the following alternatives: vsphere 5 client download
Use the VMware Public Download Repository (though less reliable for old clients): https://download3.vmware.com/software/vmw-tools/