Hello Mr. Krogloth,
Long time no see 
What actions exactly seem slow? How do you measure it?
Do you see a better performance when you open the Web Client on the server where it is installed (Google Chrome avoids an Adobe Flash installation on the server directly)?
Which browser are you using?
So far I have only seen the 5.0 logs I believe, did you install the latest version of vCenter 5.1 and the Web Client?
How many users are using the Web Client concurrently?
How large is the environment roughly (hosts, vms)?
Is it installed on the same VM as vCenter Server, Inventory Service, Single Sign On?
8 cores is actually quite alot for a vCenter 4 or 2 should be enough, less is often more in the virtual environment.
Basically the Web Client is a tomcat process with a flash interface talking to another set of tomcat services to display the inventory. So it might be useful to increase the heap memory for these processes.