Sure:

function getmax($array, curmax) {
  return $cur >= count($array) ? $curmax :
    getmax($array, $cur + 1, strlen($array[$cur]) > strlen($array[$curmax])
           ? curmax);
}

$index_of_longest = getmax($my_array, 0, 0);

No loop there. ;-)

According to phpbench:

Is it worth the effort to calculate the length of the loop in advance?

Copy//pre-calculate the size of array
$size = count($x); //or $size = sizeOf($x);

for ($i=0; $i<$size; $i++) {
    //...
}

//don't pre-calculate
for ($i=0; $i<count($x); $i++) { //or $i<sizeOf($x);
    //...
}

A loop with 1000 keys with 1 byte values are given.

(time in µs)

So I personally prefer to use count() instead of sizeof() with pre calc.

As alternative you can use array_map

<?php

$strs = array('abcdefgh', 'defghjklmn', 'ghjefggezgzgezg');
$max = 5;
$strs = array_map(function($val) use ($max) {
    if (strlen($val.'') < $max) return $val.'';
    return substr($val.'', 0,$max-3).'...';
},$strs);

var_dump($strs);

EDIT implicit casts added to cast object to string

PHP doesn't have a concept of arrays. It has ordered maps which it calls arrays. They have no finite size. You can't have a fixed size array unless you use the SplFixedArray class

To create PHP's "array" you can use the following syntax.

$myArray = [];

To add elements you use keys. This will map one value to another.

$myArray['myKey'] = 'My string';

You can also use numerical keys or append a new value to the map.

$myArray[42] = 'My string of 42';
$myArray[] = 'Appended value'; // the key will be generated by PHP and will be the next available numerical value