Php: Add variable amount days to Y-m-d date format

i'm trying to add days to a date with the 'Y-m-d' format:

$oldDate = '2013-05-15';
$newDate = date('Y-m-d', strtotime($oldDate. " + 5 days"));

This ouputs '2013-5-20', but below:

$oldDate = '2013-05-15';
$addedDays = 5;
$newDate = date('Y-m-d', strtotime($oldDate. " + $addedDays days"));

doesn't work, it only outputs '1970-01-01', which doesn't make sense because i only tried to put the days to be added in a variable. They're basically the same code. I appreciate the help trying to understand this. Thanks!