You could use modulus for this one. You should calculate how many items you need per column. And then create a close and open div for example:
<?
$linksPerColumn = 4;
if ($linkCount > 4){
$linksPerColumn = ceil ($linkCount / $amountOfColums);
}
$linkCounter = 0;
?>
<div class="slide-background">
<div class="slide">
<?
foreach ($links as $link)
{
$linkCounter++;
?>
// Do your HTML Here.
<?
if($linkCounter % $linksPerColumn = 0)
{
?>
</div>
<div class="slide">
<?
}
?>
</div>
</div>
// Rest of the HTML here.
I think this should do the trick for you.