Are you on maintenance for the software? I'm assuming you are since you can download the 10.5.1 from Myesri. You may need to contact tech support for your particular issue.
Do do you have any other software installed on your machine that uses the Flexlm software or that needs a sentinal drive? Erdas/imagine/Hexigon (I think that is the new company name) software is one that comes into mind. There may be a conflict t may take some research to get both to work (I have been able to get them both to work on my desktop)
however, one last suggestion...make sure you totally uninstalled the previous lm, and then rename the folder so it has to rebuild. I would take a copy of the folder before the un install.