I am presuming that your device doesnot support SD-card (memory-card). You can see MTP, it means that drivers are fine.
Update your TWRP [TWRP for LG Nexus 5][1]TWRP for LG Nexus 5
Update your drivers and reboot PC.
Format Data from Wipe option in TWRP.
Connect to PC, and hope you can see MTP. Copy CM12 (for your device ONLY) ROM from PC to internal storage. Don't forget Gapps and Supersu zip files too.
Flash ROM first, then gapps and finally Supersu.
Reboot phone, Done.
If above steps doesnot work, then last thing you can do, is to go to bootloader and flash ROM using sideload. [1]: http://twrp.me/devices/lgnexus5.html