You could do this with the modulo operator.
$posts = get_posts($args);
$html="<ul>";
$limit = 5;
$i = 1;
foreach ($posts as $post) {
$html .= '<li>' . $post->post_title . '</li>';
if($i % $limit == 0) {
$html .= '</ul><ul>';
}
$i++;
}
$html .= '</ul>';
echo $html;