Get category title and posts through WP_Query

wp_query_category.php

<?php
$args = array(
  'cat' => set_your_id,
  'posts_per_page' => set_your_posts_per_page_ex_5,
);
// Get the category object with properties
$category = get_category( $args['cat'] );
// Define WP_Query withe the arguments
$query = new WP_Query( $args );
?>

// Get the category title
<?php echo $category->name ?>
// Get the category descriptions
<?php echo $category->description ?>

// Loop through the posts
if ($query->have_posts()) {
  echo '<ul>';
  while ($query->have_posts()) {
    $query->the_post();
    echo '<li>';
    echo '<p>' . the_time('F d, Y') . '</p>';
    echo '<h2>' . get_the_title() . '</h2>';
    the_excerpt();
    echo '</li>;
  }
  echo '</ul>';
  wp_reset_postdata()
} else {
  // no posts found
}
?>