A quality 400W PSU with one PCIE connector for the 5770 and a quality 500W PSU with two PCIe connectors for the 4870 is recommended.
A 5770 can pull 110W(9A) (more or less) at full load.
A 4870 can pull 200W (17A) (more or less) at full load.
Yours is a multi-rail design PSU. It can deliver 20A on the +12V1 and 18A on the +12V2.http://www.hipergroup.com/products.php?lv=3&cate=1&type=30&pid=12
As Davcon has said, your PSU has power enough (it can deliver 30A/360W (aprox.) on the +12V output).