Number of posts in a category

You could always do something like this:

$the_test_cat = get_category('5');
$test_count =  $the_test_cat->category_count;

Or with the template tag, wp_list_categories():

List all categories with post count
wp_list_categories('show_count=1');

List category 5 with post count
wp_list_categories('include=5&show_count=1');

Or use the Category Widget with the Show Count checkbox checked.