Maybe your old PSU was enough before, but new graphics card consumes more power and overloaded it.
For 5770 model in AMD site there is following requirement:
450 Watt or greater power supply with one 75W 6-pin PCI Express® power connectors recommended (600 Watt and two 6-pin connectors for ATI CrossFireX™ technology in dual mode).
After all it is your computer do as you wish.
