Whilst admation does not give you the ability to permanently delete files from the Ad Storage or Asset Library, you may be able to archive files that you no longer need to see in your search results.
To archive your assets, head to the relevant digital library and hover over the item that you would like to archive. Click the Information Button on the item you would like to archive.
Alternatively, you can View More Information from the preview screen.
On the resulting page, with the right account permissions, you'll see the option to click Archive on the right side of your screen.
Your account needs to have specific permissions enabled to see this button. If you can't see it, have a chat to your manager about archiving the asset for you. Note that this action is irreversible, so think carefully before archiving your assets.
Locating Archived Items
Archiving files pops obsolete files into a separate section of the digital library. To see them again, you consciously need to use filters to Include Archived Assets in your search results.