How to update OS X Version 10.9.5 to resent system update?

Back up your data, check your applications for compatibility, and depending on which MacBook Air model you have, download El Capitan, High Sierra, or Catalina.

uwu_senpai: As stated in the list of exceptions, that method cannot be used to upgrade from 10.9.5.

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Perhaps use the blue links already posted to read what Apple has to say.

Your hardware may also be the key to how recent a macOS it can use.

Avoid the latest and greatest, unless you start over with all newer software

and peripherals that use only 64-bit software, and have no 32-bit drivers.

Catalina 10.15. requires newer 64-bit stuff. Mojave 10.14.6 is still available,

just prior to Catalina. You'd have to look; & won't be in your system update.

High Sierra 10.13.6 too is a choice. These Installers are found in Support links.

An older Mac may have to settle for El Capitan, if it cannot be upgraded.

Since I do not know which OS you would like to go to the only thing I can say is that you can do a reinstall of the OS through internet recovery. This will let you update your Mac to the latest OS that your Mac is compatible with. How to reinstall macOS from macOS Recovery - Apple Support

There's some relevancy to the situation in this similar topic and reply:

• Upgrade from Mavericks to Catalina hangs - Apple Community

https://discussions.apple.com/thread/250993209?answerId=251941627022#

Also plenty of valid information requiring reading & study already added here.

Between that which is & need tried, you've adequate paths to investigate.

Good luck & happy computing!🌞🌤

This read should help you: https://support.apple.com/en-us/HT201475