How to query the last 5 nodes of multiple content types?
I think the only thing you need is alter the second line of your EntityFieldQuery to this:

-&gt;entityCondition('bundle', array('typeA', 'typeB', 'typeC', 'typeD'), 'IN')


Haven't tested this particular though, but you can query multiple content types this way.

Cheers

EDIT: Maybe this can help you more: https://www.drupal.org/node/2048345