I haven't tested AcyMailing 8 thoroughly with Joomla 5 yet, so I can't confirm that it is working correctly in all segments and features.
From what I understand you can install Acymailing on Joomla 5 without issues, but with the current version upgrading your Joomla 4 with Acymailing installed to Joomla 5 you have to follow this extra step.
The new "Behaviour - Backward Compatibility" will take care of this once the installation is finished, but as this plugin is not available on the upgrade of Joomla it crashes the site and leaves it in a crashed state.
So before updating to Joomla 5 first disable all acymailingplugins, do the upgrade (Joomla will automatically enable the "Behaviour - Backward Compatibility" plugin) and after the update you can publish the acymailing plugins again.
Always make sure you have a backup before upgrading your website
Our developers are aware of this and will work on a solution.
On the other hand, Joomla 5 has just been released. I would stay away from it for at least the first couple of releases, until all the first bugs and issues are being fixed in it.