Clearing the cache breaks the installation
You need to check the PhP error logs on your server for the reason for the 500 error.

A quick guess would be that your backup excluded the actual cache table structure and not just it's contents.  So when the code needs to access one or more of the tables, it is not there.  The log should show you the specific problem.

An alternative would be to use something like MySQL Workbench and working / non-working databases and start comparing tables between the two.  Missing tables should be fairly obvious.