if (have_posts()) :

    $args = array(
        'showposts' => '5',
        'paged' => $paged
    );


    $thePosts = query_posts($args);
...

if (have_posts()) :

        $args = array(
            'showposts' => '5',
            'paged' => $paged
        );


        $thePosts = query_posts($args);


         global $wp_query;
         echo $wp_query->found_posts;
    ...

Search Result for

<?php
/* Search Count */
$allsearch = &new WP_Query("s=$s&showposts=-1");
$key = wp_specialchars($s, 1);
$count = $allsearch->post_count; _e('');
 _e('<span class="search-terms">');
echo $key; _e('</span>');
_e(' &mdash; ');
echo $count . ' ';
 _e('articles');
 wp_reset_query();
?>

$args = array(
    'cat'=> $cat,
    'posts_per_page' => 10,
    'paged' => $paged,
    's'=> $s
  );
  query_posts($args);

  $startpost=1;
  $startpost=10*($paged - 1)+1;
  $endpost = (10*$paged < $wp_query->found_posts ? 10*$paged : $wp_query->found_posts);
        ?>
  <h2 class="displayResult">Showing results <?php echo $startpost; ?> - <?php echo $endpost; ?> of <?php echo $wp_query->found_posts; ?></h2>

if (have_posts()) :

    $args = array(
        'showposts' => '5',
        'paged' => $paged
    );


    $thePosts = query_posts($args);



     echo $thePosts ->found_posts;
...