I tried re downloading Lightroom 5 on my Mac after it crashed in Develop Module but when it tries to open, it bobs in the dock, turns into the red Adobe logo (when the mouse hoovers it says PDApp) and then closes out before anything opens. I tried several times to download it from the internet and the same thing happens when I use the original CD I bought.
I'd recommend you to use the Adobe Cleaner tool to remove existing Lightroom 5 and then reinstall it. See Use the Creative Cloud Cleaner Tool to solve installation problems
Download link for Lightroom 5: - Download Photoshop Lightroom