There hasn't been a Lightroom update since the D5500 was released. I suspect it will be added in the next update or upgrade. In the meantime, you can use DNG converter 8.8 to create digital negative copies that can be opened with the current versions of Lightroom.
Lightroom is up-to-date simply means it's the latest version released by Adobe.
However, Lightroom (even the up-to-date version) does not yet support the D5500
As an interim measure, you can use the free Adobe DNG converter 8.8, convert all D5500 NEF files to DNG format then edit the DNGs in Lightroom 5.
Support for the Nikon D5500 was released with Adobe Camera Raw 8.8 on March 19th 2015. There has not been a corresponding release of LR 5.8. The expectation is that LR 6 will be release in the near future but there has been no specific release from Adobe.
In the meantime LR users have been advised that they can make use of the Adobe DNG Converter 8.8 which they can use to convert the NEF files to the DNG format and import these files for use in LR 5.7.1 or other earlier versions.
See the link below for the official communication.
Quote from the communication. "Camera Raw 8.8 is now available as a final release for Photoshop CS6 and Photoshop CC. DNG Converter 8.8 is provided for all Lightroom customers and Photoshop customers using versions of Photoshop older than Photoshop CS6."
It is clear that there will be no further versions of ACR version 8. and unlikely to be a version 5.8 for Lightroom. We have to await Photoshop CC 2015 and LR 6.
thanks for the help guys.