If your phone is not supported anymore (Nexus 5) you can install a custom rom to have all security related updates on it.
It first the phone must have an unlocked boot loader.
Download twrp from: https://twrp.me/devices/lgnexus5.html
Rename twrp-3.0.2-0-hammerhead.img → recovery.img Open a terminal and type:
adb reboot bootloader fastboot flash recovery d:\Nexus5_backup\recovery.img fastboot reboot
Make sure to hold directly volumn down + power.
Now select recovery mode and you should see the new recovery image loaded.
Connect a OTG usb adapter and a USB stick (formatted with FAT32). In TWRP select backup and select OTG as backup destination.
Install custom rom
I use the pure nexus project: http://forum.xda-developers.com/google-nexus-5/development/rom-pure-nexus-substratum-t3477787