Why new client cant connect old ones (5.0 or 5.1 series)
Actually it can connect. Unless you are using WinXP or Win2k3 for which there is a workaround you have to use:
http://tsmith.co/2013/xp-cant-connect-via-vsphere-5-5-c-client/
Yes correct. You can connect. 5.0/5.1/5.5 ESXI host by using 5.5 VI client.
did you mean VI = Vsphere Client ?
I have 5.0 host and I dont wanna download and install Vsphere Client 5.0
But Vsphere client 5.5 on the host connection get the upgrade window
Why Vsphere client 5.5 cant connect to 5.x host ?
If the 5.5 is progress i cant see any progress on client side.
Each version (5.0, 5.1 and 5.5) has it's own vSphere Client. You can install all of them on the same client though. What happens when you start the client, is that a launcher application is started, which chains the correct client after detecting the ESXi host version.
André