I totally think the birds go into the mix extremely well. They pick up the white and pink of the first floral and if birds don't go with flowers and vines just shoot me now. LOL
For a dark, I would go with the deep rose color that appears in both of the floral fabrics. I would never want to add black to such a pretty airy assortment of fabrics.
If I were going for a 6th color, I'd look for something in a pink and turquoise to pick up those tones out of the 2nd floral and the other 2 prints. The pretty carnation pink, not the deeper tones.