How can I ensure iPencil 2nd Generation works properly with iPad Air 5?

First, compatibility. Verify that your Apple Pencil is compatible with your iPad:

Apple Pencil compatibility - Apple Support

Assuming that you have an Apple Pencil that is compatible with your iPad, this support page may be helpful with pairing and use of the Pencil with your iPad:

Connect Apple Pencil with your iPad - Apple Support

If you continue to experience difficulties, here is one of the better troubleshooting guides:

https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/

Be aware that if your Pencil has been set-aside for an extended period, unused and uncharged, the Pencil battery may have been damaged through deep discharge. In common with all Li-ion batteries, they must always have some level of charge.

The tiny internal Li-ion battery is susceptible to permanent/irreversible damage through being left discharged for long periods. Even some “new” pencils can exhibit signs of failure out-of-the-box if they are “old stock”. 

It is essential that if you have an Apple Pencil that you charge it regularly - whether used or not - so as to protect the battery from deep-discharge. Do not allow a pencil to remain in low-charge state for any period of time - as the internal battery will fail, rendering the Pencil useless. Setting aside an unused Pencil, for extended periods, is a recipe for premature death of the Pencil battery.

If the Pencil Battery has failed, the only remedy is to replace the Pencil. If the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced by your retailer or at an Apple Store.

Genius Bar Reservation and Apple Support Options - Apple

Gentle warming of the Pencil (such as placing on a hot water radiator), prior to attempting charging of the Pencil, can sometimes resurrect a dead Pencil battery.

As per this compatibility list:--> Apple Pencil compatibility , an iPad Air 5th generation supports Apple pencil 2nd or 3rd (USB-C) generation.

If you already tried (to no avail) all the steps provided in this support article:--> If you can't pair Apple Pencil with your iPad , I suggest that you contact Apple Support directly, using this link:--> Contact Apple for support and service , or make an appointment (*) and have your device+pencil inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> https://locate.apple.com/choose-country-region . After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.