can anyone help me recover my light room serial number
Did you try looking in your online Adobe account?
Adobe Account: Your Products
It would be there if you purchased direct from Adobe, or ever registered your software.
if you still have access to your old installation you can find the serial number in a file called "Lightroom 5.0 Registration.lrreg" (location MacOS: /Library/Application Support/Adobe/Lightroom/, Windows.C:\ProgramData\Adobe\Lightroom\).
Retrieving data ...