I see no reason why templates should have any issue with Joomla 5. Changes in Joomla 5 largely focus on removing depreciated code and namespacing with fields and xml which should have no bearing on the frontend at least. There is some frontend issues with namespacing but these should not be an issue once you have the Behaviour - Backward Compatibility plugin enabled. We will be resolving these issues in a future round of updates.

I've tested the templates mentioned here (Emani, Layla and Nina) with each templates demo content and I am unable to replicate any issues.