If your app runs fine on .NET Core 5 in Windows (not full .NET Framework), then by definition it should run on .NET Core 5 on OS X and Linux.
However that’s still too optimistic, as file paths and so on are still different enough to impact the way you write your code. Thorough testing is always needed.
solved Now that part of the .NET Framework runs on Mac and Linux, how can we know if a .NET app will run outside of Windows?