You can using app: [root] FlashFire that can downloaded in PlayStore.
Then, download the latest factory images package for Nexus 5 from here
After the file is downloaded and saved in your phone, open FlashFire app.
The app will grant root access and if it found update[OTA] file, choose 'delete'.
Next, click "plus" icon > choose "Flash firmware package" > browse to the location that you saved the downloaded factory image.
Then the app will scanning the firmware file and after that you can select some options.
*If you want to keep TWRP as recovery, just uncheck "Recovery".
*Be careful, if you want to keep your data in phone, make sure that "Data" unchecked.
Last, just click "FLASH" then your phone will reboot and install the update.
*Note: I've tried this for my Nexus 5 and it is successfull. Hope it works for you too :)