Display custom post categories and their posts - wordpress

Question

I am trying to display the category titles and their posts from a custom post type. I can get the category to display but it currently lists all the posts within the custom post area instead of separating them in to the
<?php
$taxonomy = 'staff';
$cat_args = array(
'taxonomy' => $taxonomy,
'tax_input' =>$tax_input,
'orderby' => 'name',
'order' => 'ASC',
'child_of' => 0
);
$tax_terms = get_terms($taxonomy);
foreach ($tax_terms as $tax_term) {
echo '<div class="categorybox">';
echo '<h4> <a href="' . esc_attr(get_term_link($tax_term, $taxonomy)) . '" title="' . sprintf( __( "View all posts in %s" ), $tax_term->name ) . '" ' . '>' . $tax_term->name.'</a></h4>';
$args = array(
'post_type' => 'staff',
"singular_label" => "Department",
'numberposts' => 5,
'taxonomy' => $taxonomy->$tax_term,
);
$posts = get_posts($args);
?>
<ul><?php
foreach($posts as $post) {
?>
<li><?php the_title(); ?></li>
<?php
} ?>
</ul><?php
echo '<a href="' . esc_attr(get_term_link($tax_term, $taxonomy)) . '" title="' . sprintf( __( "View all posts in %s" ), $tax_term->name ) . '" ' . '>View all articles in ' . $tax_term->name.' »</a>';
echo '</div>';
}
?>

Answer 1

There no option taxonomy in get_posts(). Try this one
'tax_query' => array(
array(
'taxonomy' => 'staff',
'field' => 'slug',
'terms' => $tax_term->slug
)
)

Answer 2

<?php
$query = new WP_Query( array( 'post_type' => 'testimonials','posts_per_page' => 10 ) ); //testimonials custom post type
while($query->have_posts()) : $query->the_post();
?>
<ul>
<li>
Category:<?php the_category(', '); ?>
<h3><?php the_title(); ?></h3>
</li>
</ul>
<?php endwhile; ?>