Displaying text if post was within 5 hours

human_time_difference() will not work here as it returns a string in a human readable form. However, we can use some of the logic used there to construct a workable function

You can try the following: (Untested)

function get_custom__time_diff()
{
    global $post;

    // Get the current time
    $current_time = time();
    // Get the post date
    $post_date    = get_the_time( 'U', $post );
    // Get the amount of seconds in 5 hours
    $test_time    = 5*HOUR_IN_SECONDS;
    $diff         = $current_time - $post_date;

    if ( $diff < $test_time )
        return 'New';

    return '';
}

You can then call it as follow inside the loop

echo get_custom__time_diff();