I have just found an alternative solution:
global $post;
$current_post = $post->ID;
$array=range(1,$current_post);
$args = array(
"numberposts' => 5,
'offset' => 0,
'category' => $category->term_id,
'orderby' => 'ID',
'order' => 'DESC',
'exclude' => $current_post,
'post_type' => 'post',
'post_status' => 'publish',
'suppress_filters' => true,
'post__in' => $array );
$posts = get_posts($args);
I’m not sure why the previous method does not work. I have resolved the problem anyway. Thank @imHavoc and @userabuser for having taken a look at my problem 🙂