The update frame is the same for any version: make a backup, check compatibility, test the environment, follow instructions update Joomla Core, and Update Joomla extensions. Test (UI/Ux), how al the features, APIs, and connections work. Make adjustments where you see the issues. However, if your website is on Joomla 3.x and you prefer to shift to Joomla 5( that is deeply recommended), you need to decide how to build the migration processes. It’s recommended to update Core Joomla from 3 to 4 first, and from 4 to 5 after. The extensions and components are usually updated on the final version (in this case Joomla 5).