Thanks for the clues. Turns out there was something in the zen directory that was overriding the global setting of PHP 5 set in the cpanel. I still don't know what it was, but I put the two lines below in my .htaccess at the zen root and it seems to have fixed things.

AddHandler application/x-httpd-php5 .php5 .php4 .php .php3 .php2 .phtml
AddType application/x-httpd-php5 .php5 .php4 .php .php3 .php2 .phtml