乱数を生成し、n個切り取る際は、range, shuffle, array_sliceで作ります。
$col = range($i * 15 + 1, $i * 15 + 15);
shuffle($col);
$nums[$i] = array_slice($col, 0, 5);
index.php
<?php
require_once(__DIR__ . '/config.php');
require_once(__DIR__ . '/Bingo.php');
$bingo = new \MyApp\Bingo();
$nums = $bingo->create();
?>
<!DOCTYPE html>
<html lang="ja">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>jQueryスライドショー</title>
<link rel="stylesheet" href="styles.css">
</head>
<body>
<div id="container">
<table>
<tr>
<th>B</th><th>I</th><th>N</th><th>G</th><th>O</th>
</tr>
<?php for ($i = 0; $i < 5; $i++) : ?>
<tr>
<?php for ($j = 0; $j< 5; $j++) : ?>
<td><?= h($nums[$j][$i]); ?></td>
<?php endfor; ?>
</tr>
<?php endfor; ?>
</table>
</div>
</body>
</html>