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>\';