In Joomla 4, the following works:

$modelcat = new Joomla\Component\Content\Site\Model\CategoryModel();
$category = $modelcat->getCategory();

In Joomla 5, it crashes with the error "Uncaught Throwable of type Error thrown with message "Call to a member function get() on null"". The exception is thrown in CategoryModel::getCategory() on components/com_content/src/Model/CategoryModel.php:338:

if (!empty($this->state->get('params'))) {

because the "state" data member is null out of the CategoryModel constructor. It worked in Joomla 4 because the corresponding line in getCategory would go instead:

if (isset($this->state->params)) {

and isset would return false if state is null.

Observed on the JA Playschool template by JoomlArt, with a menu item of type "Gallery List". Reproduces on a fresh install.