Support

You're in luck, because I forked the core reCAPTCHA plugin and updated it for Joomla! 5. You can find it at https://github.com/nikosdion/plg_captcha_google. Please do read the Usage paragraph on that page and follow its instructions. The package download is at https://github.com/nikosdion/plg_captcha_google/releases/latest. 

The One True Joomla! Way™ to use CAPTCHA is thus. Note that I am assuming you are going to be using the globally selected CAPTCHA method, and that you are using PHP 8.1 or later (matching the minimum requirements for Joomla! 5).

// ### This method goes both in your View, and your Model.
public function getCAPTCHAObject(): ?\Joomla\CMS\Captcha\Captcha
{
  // Get the default CAPTCHA plugin from the application's configuration.
  $plugin = \Joomla\CMS\Factory::getApplication()->getParams()->get('captcha', '');
  
  // Replace com_example with your own extension name
  return empty($plugin)
         ? null
         : \Joomla\CMS\Captcha\Captcha::getInstance($plugin, ['namespace' => 'com_example']);
}

// ### In your View
$this->captcha = $this->getCAPTCHAObject();

// ### In your view template ###
// Note that it creates a form field with the name "captcha".
<?php echo $this->captcha?->display('captcha') ?? ''; ?>

// ### In the form validation code of your Model ###
public function isCAPTCHAValid(): bool
{
  $input = \Joomla\CMS\Factory::getApplication()->input;
  return $this->getCAPTCHAObject()?->checkAnswer($input->get('captcha', '', 'raw'))) ?? true
}

If you are following this standard Joomla! practice for using whichever CAPTCHA is configured in the system you will have no problem using the replacement plugin or any other CAPTCHA plugin, regardless of which CAPTCHA method it's using. For example, if you decide reCAPTCHA is not for you and would like to switch the hCAPTCHA, or CloudFlare Turnstile you can do so by installing the respective plugin and selecting it as your default CAPTCHA in Global Configuration. If you don't like my reCAPTCHA plugin, you can use another one just fine.

For an example of using that in the real world, please see https://github.com/akeeba/contactus. This is the contact form component we use on this site. Find \Akeeba\Component\ContactUs\Site\Model\ItemModel::getCaptchaObject and check its uses. You will very quickly see how CAPTCHA works inside a real extension. Also note that the code in the component I linked you is more verbose as it does a lot of error handling, and is targeting PHP 7.4 to 8.4 at the time of this writing.