<p class="p-1"></p><p class="p-2"></p>
<div class="wrap"><p class="p-3"></p></div><p class="p-4"></p><p class="p-5"></p> и т.д.
(?<=<\/\w>).+<\/?p[^>]*\>(.*?)<\/p>
<?php
$html = <<<HTML
<p class="p-1">p1</p><p class="p-2">p2</p>
<div class="wrap"><p class="p-3">p3</p></div><p class="p-4">p4</p><p class="p-5">p5</p>
HTML;
preg_match_all('!<p[^>]{0,}>(.*?)</p>!si', $html, $out);
var_dump($out[0][3]);
$out[1][3]