Yeap, as far as fitting goes the Asrock N68-S has one PCI-e 16x port in which you can fit the HD5770.
Just remember to remove your GeForce 8400GS.
As for power requirements, AMD recommends a minimum of a 450W PSU for the HD5770 and one 6 pin power connector. You'll be cutting it close, no OCing, but it should be fine.
The thing which I'm worried most about is space. You used an 8400GS earlier which (as far as I know) are half-height cards. HD5770 is a full height model. If your casing cannot accommodate more than a half-height card then, it is a no go. Unless you change your case.