Rekordbox licence when laptop crashed

Yes you can. If you login on the Pioneer DJ website and click on your name you can get to license section and see the license if you used it with Rekordbox 5. 

If you use Rekordbox 6 the license won't be necessary as the DDJ-400 is a hardware unlock device when connected. So essentially a hardware version of your license key. 

You can request Pioneer DJ Support to deactivate your license via a form here.