No problem, you can directly move to 14.0 from 11.5. Just get the migration tool from 14.0 support packages. The one from 12.0 might have some issues doing this for you.
You would again get a batch file.
Get a backup of Illuminator folder and perform the migration from there after some pre-requisites like checking for URLs and file paths. As 11.5 wasn't case sensitive, but 14.0 is.
Regards,
Swaroop