Hello.
In environments with old versions of VMware vSphere there is no other option than to use a old browser that supports Adobe Flash Player.
Personally I use the following combination, but only to manage VMware vSphere, to surf the internet I use a more current browser.
Firefox ESR 38.8 (32bits)
Adobe Flash player 29.0.0.113
Both the browser and the flash player must be configured so that they are never updated.
To login using the vSphere Web Client (Flash). You can instead open a Web browser and enter the URL for the vSphere Client: https:// ip_address/ui
To login using the vSphere Web Client (HTML5) , enter the URL: https://ip_address/vsphere-client.