Lightroom 5.7.1 is an update for version 5.6 so, the base version remains the same which is version 5.
If the shortcut is missing, go to the following path in File Explorer :
C:\Program Files\ADOBE\Adobe Photoshop Lightroom 5.7.1
Look for Lightroom.exe > right click on it > choose Send to > Desktop > this will create a shortcut on your desktop.
Or, double click on that Lightroom.exe and check if it works fine.
Chetna,Thank you for your reply. I encounter this problem: when I follow the path you indicate, I do not find Lightroom.exe. I have looked under common files; the same--no Lightroom.exe. If I double-click on the lightroom 5.7.1 file, it only wants to reinstall.