Hello,
Is there any issues, with update Roundcube from version 0.5.1 to latest stable - 0.7.2? Which is best way of make such upgrade? I will try to make copy of current mysql database, make another user, grant privileges to him, make another vhost in apache to make copy of curently running mail system, and will try update to 0.7.2 on it.
There shouldn't be any problems upgrading directly just remember to backup before starting. It also wouldn't be a bad idea to read though the upgrade guide at: http://trac.roundcube.net/wiki/Howto_Upgrade
While the upgrade process generally works well, I typically do a fresh install using a copy of the original database instead. There are typically new config options that you will want to review, as well as possible plugin issues/updates. Setting up the new version as a separate instance allows you to test such things prior to going live.