Although I can find no announcement on the Adobe website, Lightroom 5.6 is available for download and it appears to include support for the Nikon D810. See Uh-Oh! I Can’t See My Nikon D810 Files. I can’t find a download page that I can link to or any information on Adobe.com at the current time. However, I will update this post once something is posted online. To update to Lightroom 5.6 if you subscribe to the Creative Cloud, quit Lightroom, start the Creative Cloud app, and click the “Install” button next to Lightroom 5. If you have a perpetual license for Lightroom, open Lightroom and go to Help > Check for Updates… Click the “Download” button and follow the instructions on the download page.
PS on July 31 at 1:19 pm: Information about Lightroom 5.6 and the links from which to download the update are at: https://blogs.adobe.com/lightroomjournal/2014/07/lightroom-5-6-now-available.html. If you subscribe to the Creative Cloud, download the update from within the Creative Cloud app.