You don't need any exporting, or importing, or discrepency checks. While you can't do an in-place upgrade, that's probably not something that you want to be doing in production. Side-by-side, or, since you say new hardware, install the new version on the new hardware directly. Safer, as if something goes wrong it doesn't take the old version out.

Then, backup the SQL 2005 database and restore it to the new 2016 instance.