How to upgrade Android 7 operating system in Honor 5X mobile?

Honor is expected to get updates from Google for the period of 24 months from the date of launch. From that point of view, I would ask you to wait till the further confirmation form the manufacturers. Ideally, no smartphone manufacturer offers you a clear time frame for the update schedule. You can only keep waiting.
Having said that, if you want to get the update before it is officially available, you can choose to install custom ROM on your device. Please note that installing a custom ROM is a risky procedure which needs you have a thorough understanding of the steps involved. If anything goes wrong, you run the risk of bricking your smartphone. I would advise you to proceed with caution.
First of all your device needs to be rooted. For rooting instructions, you may need to refer to the tips in a related thread on this site. Rooting instructions remain almost similar across devices. Once you are sure that you are rooted, follow the steps below -

• Make sure your battery is at least at 50 percent
• Download the nougat ROM for your device from the source you wish to. There are a host of custom ROMs available. Explaining each of them is outside the purview of this thread.
• Copy the the downloaded zip file to your SD card
• Boot into recovery. The procedure will depend upon your phone model. Generally, pressing Volume Up and Power key simultaneously should do that.
• Chose Wipe, then Wipe data/factory reset
• Now choose Install. Navigate to the zip file saved above.
• Confirm installation. It should take a while to complete installation of the custom ROM.
• Once the ROM is installed, tap on Reboot system. The device will take around 3 to 5 minutes to reboot.

And that would do it. Your smartphone is updated to the Android Nougat OS. Please note that custom ROMs void your warranty. Also note that the ROMs installed in such way may be unstable in some cases.
I would suggest you to consult an expert if you are not familiar with rooting and installing custom ROM.

It is possible to update Android version in Honor 5X to Nougat.

You have two options in this case.

Install CM14 on Honor 5X

Cyanogen Mod is officially deprecated. And it will be no longer supported. If you are techie and know how to use phone with deprecated ROM then this can be one good option.

1. Download CM14 from the git repository of Cyanogen.
2. Boot into root,backup your device and then wipe the disk.
3. Factory reset the device and then in recovery console access "update.zip".
4. In recovery console, start the installation through the menu.
5. Let the system update and install the ROM.
6. Reboot.

This method is a bit cluttered now considering any server calls to cyanogen will be called off. And you may have plenty of broken notifications.

Update to Nougat 7 using default Android ROM

This ROM can be downloaded through default android website or the XDA developers. Here are the steps that you can use to update the Honor 5X to nougat update.

1. Download the update to nougat from here :

http://forum.xda-developers.com/honor-5x/development/rom-official-mokee-source-project-t3505600

or https://forum.xda-developers.com/honor-5x/development/rom-lineageos-14-1-pre-official-kiw-l24-t3528488

2. Download the update on device SD card as well as on PC (just to be safe).
3. Save the update with the filename update.zip.
4. Reboot into the Honor 5X recovery into TWRP recovery mode.
5. Inside the recovery mode, wipe the data but before that backup if you have any files.
6. Now go to install option.
7. Navigate to the zip file you just downloaded in SD card.
8. Start the installation.
9. After completing the installation, reboot your device.

That's all.

Do understand the fact that your warranty will be void after installation through either of this method. Another thing is that you may find that your default call to honor's server won't be processed from now on. Instead you'd be getting further patches from the ROM company that you have installed. Unless you are into experimentation and don;t mind bricking your device, better stick with the old update on the Honor 5X.