Included with Guitar Rig 5 should be a CD. Insert the CD into your computer, and run the installer program, such as Guitar Rig 5 Setup PC. The Guitar Rig 5 VST plugin should be located at C:\Program Files\Native Instruments\VSTPlugins\Guitar Rig 5.dll.
I've found Reaper to be a bit spotchy when it comes to adding multiple plugins. The best way I've found to ensure that already added plugins do not get removed when adding a new plugin is to place every plugin .dll file in the C:\Program Files\REAPER (x64)\Plugins directory and to then select Options > Preferences > VST > Re-scan or Clear cache/re-scan.
IMPORTANT - Do not provide C:\ as the base search directory, as this will search the entire PC for .dll files, which caused big problems for me (I had to uninstall and then reinstall Reaper).