ACR 8.8 does support D5500, LR does not (yet). You'll have to wait for the next LR release which will probably be LR6 ... don't ask when it will be released before searching the forum for LR6 topics.
You can use the latest, free DNG converter which uses ACR 8.8 and then import the DNG as a workaround meanwhile.
LR will handle NEF files conerted to DNG or use Nikon software appropriate to the D5500 to create tiffs and import those into LR.
Windows download (.exe file) click here DNG Converter 8.8
Mac download (.dmg file) click here DNG Converter 8.8
You can convert a whole folder of raw images in one click. See this quick video tutorial: