math.php

<?php

$source = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9];

for ($i = 0; $i < count($source); $i++) {
    for ($j = 0; $j < count($source); $j++) {
        if ($j == $i) {
            continue;
        }
        $numA = intval($source[$i] . $source[$j]);
        if ($numA < 10) {
            continue;
        }

        for ($k = 0; $k < count($source); $k++) {
            if ($k == $i || $k == $j) {
                continue;
            }

            for ($l = 0; $l < count($source); $l++) {
                if ($l == $k || $l == $i || $l == $j) {
                    continue;
                }

                for ($m = 0; $m < count($source); $m++) {
                    if ($m == $l || $m == $k || $m == $i || $m == $j) {
                        continue;
                    }

                    $used = array($i, $j, $k, $l, $m);

                    $a = intval($i . $j);
                    $b = intval($k . $l . $m);

                    if ($b < 100) {
                        unset($used);
                        continue;
                    }

                    $result = $a * $b;

                    if ($result < 10000 || $result > 99999) {
                        unset($used);
                        continue;
                    }

                    $result .= '';
                    $result = str_split($result);
                    $result = array_map('intval', $result);

                    if (count(array_unique($result)) !== 5) {
                        unset($used);
                        continue;
                    }

                    if (count(array_diff($used, $result)) !== 5) {
                        unset($used);
                        continue;
                    }

                    var_dump(
                        sprintf("%d%d * %d%d%d = %d%d%d%d%d", $used[0], $used[1], $used[2], $used[3], $used[4],
                            $result[0], $result[1], $result[2], $result[3], $result[4])
                    );
                }
            }
        }
    }
}