You should not be using a USB cable to pair your USB-C Apple Pencil. Just to be sure, there are four Apple Pencil models: 1st generation, 2nd generation, USB-C, and Pro. I am assuming you got the USB-C model which is compatible with your 5th generation iPad Air ... correct?
Let's go over the pairing process just to make sure you didn't miss a step.
- Make sure your iPad is unlocked and awake.
- Connect the Apple Pencil (USB-C) directly to the iPad’s USB-C port. Don’t use a cable between them. Apple specifically notes the Pencil should plug directly into the USB-C port to pair. Using a USB-C to USB-C cable in between often causes pairing to fail.
- Once it’s plugged in, you should see a “Pair” prompt pop up on the screen.
- Tap “Pair” to complete the process.
- After pairing, you can remove the Pencil. It should now remain connected via Bluetooth. You can now use it wirelessly.