<?php
$res=$mysqli->query("SELECT id,GROUP_CONCAT(client_id) as clients FROM services WHERE id = 3 GROUP BY id");
$row = $res->fetch_array(MYSQLI_ASSOC);
$result = $row['clients']; // $row['clients'] contains string 5,6,7
$res->free();
 
$resclients=$mysqli->query("SELECT id,client_name FROM clients WHERE id = IN ($result)");
// handle $resclients
 
?>