I cannot find it from my account (only the LR3 and LR4 information is provided). In the program itself the last digits are covered. I have ordered the LR5 as the digital version.
Launch Finder and click the Go menu whilst holding down the Opt(alt) key and choose Library
(n.b. the library is hidden until you press alt) then go to:
/Application Support/Adobe/Lightroom/Lightroom 5.0 Registration
Click choose application and select text editor then click open.
Click the Windows start button and in the search box type:
%ProgramData% and hit return; then navigate the following path
C:\ProgramData\Adobe\Lightroom\Lightroom 5.0 Registration.lrreg
Inside the Lightroom folder right-click on Lightroom 5.0 Registration.lrreg and choose open.
Choose “Select a program from a list of installed programs” then click OK
Select Notepad or click the Browse button to find Notepad
When the registration file opens in Notepad you will see your serial number.