I use Sitefinity version 5 in medium trust enviroment but get security exception.
[SecurityException: That assembly does not allow partially trusted callers.]
The problem is coming from some security settings on your environment. As MSDN says regarding the error:
Only applications that are fully trusted by the runtime code access security system are allowed to access a shared managed code assembly that is not explicitly marked with the System.Security.AllowPartiallyTrustedCallers attribute. A partially trusted assembly (one that is registered in SQL Server with the SAFE or EXTERNAL_ACCESS permission set) that attempts to access a strong-name signed assembly without this attribute causes a System.Security.SecurityException to be thrown.
Also please ensure that Sitefinity is running in Full Trust environment. If you still experience issues with your shared hosting provider I can suggest you is to navigate to our Hosting Partners page and choose a hosting parting from the list - they are certified to run Sitefinity without having you to experience such errors.
the Telerik team