Help in query for list links

Try it like this:

$dates = array(); // declare an array to hold dates

echo '<ul>';

if (have_posts()) : while (have_posts()) : the_post(); 

    $thisday = get_the_time('m/d/Y'); // this post's date

if (!in_array($thisday,$dates)) { // check if it's in the array
    echo '<h5>Date '.$thisday.'</h5>'; // if not, print header with date
    $dates[] = $thisday; // and store it
}

echo '<li>';
the_category();
echo '</li>';

endwhile;
endif;

echo '</ul>';