No, you can download the MAC version from Product updates
and then use your existing LR 5 serial number
No, the Lightroom license is cross-platform. You can just download Lightroom 5 for the Mac and install it. Then use the serial number you already have.
Adobe - Lightroom : For Macintosh : Adobe Photoshop Lightroom 5.6
If you are planning on moving your work from the PC to the Mac, this might help:
How do I move Lightroom to a new computer? | The Lightroom Queen
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