It is certain that Google will not release Android 7.0 Nougat update for Nexus 5. However, developer communities are busy developing Android 7.0 Nougat AOSP ROM for Nexus 5. A first build of Android 7.0 Nougat custom ROM is now available for Nexus 5 that you can tryout right now on a rooted phone.
The AOSP Nougat port for Nexus 5 is an early Alpha build. For now, mobile connectivity (RIL), Wi-Fi and audio are working fine, but many other functions, such as Bluetooth, camera, etc. are not working. The developer may work more on this ROM to make it a fully working Android 7.0 Nougat AOSP ROM for Nexus 5.
Interested tech-savvy users can download and install the Android 7.0 Nougat AOSP ROM on Nexus 5 via TWRP recovery. Head over to the XDA forum [HERE], download the ROM and flash it via TWRP recovery. Keep in mind that this is an early Alpha build released for testing purpose, so it cannot be used as a daily driver.
Here is quick guide to know how to install Android 7.0 Nougat AOSP ROM on your Nexus 5. First things are your device should be rooted and TWRP recovery installed on it. Then, download the ROM zip file, save it into the phone storage.
Now, boot your phone into TWRP recovery, wipe data/factory reset, then select Install, choose ROM zip file and flash it. Once done reboot your phone. At first boot, Bluetooth will show a force close, just ignore it. (source – XDA)