for the idea of storing data on the provider webside, it’s a good idea but I recommend to use JSON onstead of XML. it’s a litte bit faster to parse and you will save a litte bit bandwith
on the provider side, you can use the WordPress AJAX helpers to make somethig like that :
add_action("wp_ajax_nopriv_logoData", function () {
$data = array(
"text" => "the new logo",
"url" => "http://provider-server/wp-content/logo6.png";
);
echo json_encode($data);
exit();
});
and on the client side (the 5 websites), you can do that to receive data :
$response = wp_remote_get("http://provider-server/wp-admin/adin-ajax.php?action=logoData");
$data = json_decode($response);
var_dump($data); // will show the array with the data