After several upgrades my Concrete5 instance is totally corrupted.
Can I remove concrete5 and app licences from my the current installation, drop everything and apply licences again to a new instance?
Go to your profile page and click on 'Projects' then at the bottom of that page click on 'Release From Project' for all of your addons.
Then when you have rebuilt your site you can go back and assign them to your project.
If you are going to create your new site on a different domain, just add the new domain as a new project and assign the the addon licenses to your new project.
Once you have released the addons from the project, you can go to your profile page click on Transactions and then click Licenses, you will be able to download your addons so you can manually install them to your new site.